Evaluation Home Page |
| Information on mass chains and nuclides |
|
 |
3H (2010PU04)
GENERAL:
Ground State:
μ = 2.978960 ± 0.000001 μN
Mass Excess, M - A = 14.9498060 ± 0.0000023 MeV
T1/2 = 12.32 ± 0.02 y = 4500 ± 8 days
Decay Mode: β- decay
Binding Energy, EB = 8.481798 ± 0.000002 MeV
Neutron Separation Energy, Sn = 6.257233 ± 0.000002 MeV
The ground state wave functions for 3H and 3He consist mainly of a spatially symmetric S state (about 90%), a mixed symmetry S' state (about 1%), a D state (about 9%) and a small P state (less than 0.1%). Some references that illustrate this are (1986IS01, 1987ER07, 1993WU08, 2002HO09) in addition to those given in (1987TI07). Note: The P state results from two nucleons each having one unit of orbital angular momentum coupling to a total of one unit of angular momentum and positive parity.
The energy of the ground state of 3H, -8.482 MeV, results from the difference between two much larger numbers. For example, Table 2 in (1993FR18) has < T > = 45.7 MeV and < V > = -53.4 MeV, using the AV14 NN interaction and < T > = 41.6 MeV and < V > = -49.3 MeV, using the NIJM NN interaction. When a three-body interaction is included, the following values are obtained using the AV14 NN interaction and the Tucson-Melbourne NNN interaction (1997NO10): < T > = 49.3 MeV, < VNN > = -56.5 MeV, < VNNN > = -1.3 MeV.
Also shown in (1997NO10) are graphs of the two nucleon correlation function for 3H for various NN interactions. This function gives the probability that a pair of nucleons is separated by a distance r. The calculated correlation functions all peak at separations of about r = 1 fm and drop to a tenth of the peak value at about r = 3 fm. When the NNN interaction is included, the effect on the correlation function is to increase its value near the peak. The NN interactions that are more repulsive at short range have smaller correlation values for r < 1 fm, for the NN interactions that are less repulsive at short range, the correlation values are larger for small r. In turn, the strength of the NNN interaction required to give the correct 3H binding depends on correlation values for small r in that the NN interactions that are less repulsive for small r require smaller NNN strength factors; see Table 3 and Fig. 2 in (1997NO10). These authors also calculated the probability of a nucleon being a distance r from the center of mass with and without the NNN interaction. They found that the addition of the NNN interaction increased the probability slightly for r < 1, especially around r = 0.5 fm.
In an asymptotic sense, the ground state of 3H can be considered to be composed of a spin 1 deuteron and a spin 1/2 neutron bound with an energy of -6.257 MeV. The total spin and relative angular momentum of these two clusters could be either S = 1/2, L = 0, or S = 3/2, L = 2 and still form Jπ = 1/2+. These two states are referred to as asymptotic S and D states, respectively. Given that the energy and angular momenta of these states are known, the mathematical forms of the asymptotic radial functions are known. The only unknowns are the normalization constants of the asymptotic S and D states, CS and CD. The ratio CD/CS is called the triton asymptotic ratio, ηt. There are several ways by which ηt can be experimentally determined. One such method is illustrated in (1992DA01, 1993GE04, 1994KO29). In these works, neutron pick-up reactions using polarized deuterons at sub-Coulomb energies are performed on medium weight nuclei; an example from (1992DA01) is 119Sn(pol. d, t)118Sng.s. with Ed = 6 MeV, which is 33% below the Coulomb barrier. Differential cross sections and TAP's were measured and analyzed using finite range DWBA. The calculated analyzing powers are quite sensitive to changes in ηt, which makes it possible to obtain reasonably accurate values of ηt. The weighted average of the results for ηt from (1993GE04) who obtained ηt = -0.0431 ± 0.0025 and from (1994KO29) who obtained ηt = -0.0411 ± 0.0018 is ηt(ave.) = -0.0418 ± 0.0015; the weights used were the inverse of the squares of the errors. Earlier experimental values for ηt including values obtained by different techniques are given in (1988WE20, 1990EI01, 1993GE04). An early calculation of this ratio for several models using the Faddeev method is reported in (1993WU08). See also (1997KI17). The analogous case in 2H has ηd = 0.0256; see Table I in (1998CA29). In (1990EI01), the authors discuss the physical origin of the opposite signs of ηd and ηt. They also discuss the possible presence of an additional phase factor which gives ηt a positive sign in some formalisms.
For the relationship between ηt and the analogous quantity in 3He, see the section on the ground state properties of 3He.
See reaction 2 where evidence of an excited state in 3H at about 7 MeV excitation energy is reported.
A theoretical study of virtual Jπ = 1/2+ states in 3H and 3He is reported in (1999CS02). The authors obtain such states at E = -1.62 MeV in 3H relative to the d + n threshold and E = (-0.43 ± i 0.56) MeV in 3He relative to the d + p threshold. The authors also report an unpublished preliminary analysis of scattering data with approximately the same results.
| 1. 3H(β-)3He | Qm = 18.5912 keV |
Half-life measurements for the decay of 3H are reviewed in (1975FI08, 1978RA2A, 1990HO28, 1991BU13, 2000CH01, 2000LU17). The half-life value reported in (2000LU17) is 4500 ± 8 days or 12.32 ± 0.02 years. The latter value is chosen by Audi, et al. (2003AU02). The authors of (2000LU17) recommend expressing the tritium half-life as 4500 ± 8 days since the day unit is exactly defined in terms of the second. The value reported in (2000LU17) is the average of about a dozen measurements using different techniques.
The Q value for this decay as given in (2003AU03) is 18.591 ± 0.001 keV. In reference (1993VA04), the 3H-3He mass difference is given as 18.5901 ± 0.0017 keV as measured using the Penning trap mass spectrometer. This is the value used by the Mainz Neutrino project from which the endpoint energy of the β- spectrum is obtained; see (2005KR03). Table II in reference (1993VA04) contains results of measurements of the 3H-3He mass difference with references and measurement methods. For more on the Q value of 3H decay and the measurement of neutrino masses, see (2006OT02).
It was during the time period covered by this evaluation that the question of the existence of an electron anti-neutrino with a mass of 17 keV arose. The β-decay of 3H played a major role in these studies. It is now generally considered that no such anti-neutrino exists, but many useful experimental and theoretical studies came about as a result of the question being raised. The complete story is told in (1995FR27).
On-going precision studies of the endpoint region of the β- spectrum from 3H decay have been carried out with the goal of either measuring the mass of the electron anti-neutrino or at least setting upper limits on the mass. The review (1988RO21) gives an overview of the status of these experiments as of 1988. The value of the upper limit of the electron anti-neutrino mass continues to get smaller as the experimental techniques undergo greater refinement. For example, the Los Alamos group, who used gaseous molecular tritium, lowered the upper limit from 27 eV in 1987 to 9.3 eV in 1991; see (1987WI07, 1991RO07). Two experimental groups that have continued to pursue these studies are the Mainz Neutrino project and the Troitsk nu-mass experiment. The Mainz project uses a cold, thin film of molecular tritium; the Troitsk experiment uses tritium gas. For details about the Mainz experiment, see (2005KR03) and references therein and, for the Troitsk experiment, see (2002LO11, 2003LO10) and references therein. Recent values of the upper limit of this mass from both groups are just over 2 eV; see (2003LO10, 2005KR03, 2008CA1C).
The reference (2005KR03) gives a brief historical account of laboratory studies of neutrino masses and mass differences of neutrino flavors obtained from studies of neutrino oscillations. The same reference also refers to a study using cosmological data that suggests that the actual mass of neutrinos is around 0.2 eV. The Mainz and Troitsk experiments are not able to reach this level of sensitivity. In the references (2003LO10, 2005KR03), a planned 3H(β-) decay experiment called KATRIN is described which is expected to be sensitive enough to explore this mass range for the electron anti-neutrino. For more on neutrino masses in general and the KATRIN experiment in particular, see (2006BI13, 2008OT03).
Two different approaches to determining the mass of the anti-electron neutrino emitted in the beta decay of 3H have been proposed in (2010JE1A). In one case, they consider the two-body decay in which the emitted electron is captured in a bound state of the 3He+ ion and the anti-neutrino mass is determined from a measurement of the speed of the recoiling 3He atom. In a second method using ultra-cold tritium, they propose measuring the momenta of the outgoing electron and 3He+ ion from which the mass of the anti-neutrino can be determined. The authors consider the second method to be the most promising.
Over the years, there have been several studies addressing the question of the extent to which the environment affects the 3H(β-) decay spectrum. The fact that the Q-value for 3H decay is only 18.6 keV causes this to be of particular concern; the typical β-decay Q-value is larger than this by a factor of 40 to 100 or more. (A counter example is the β-decay of 187Re, the Q value for which is 2.47 keV.) The usual treatment of 3H(β-) decay has the electron and the anti-electron neutrino both produced in continuum states and the residual 3He nucleus recoiling with a maximum kinetic energy of about 3.4 eV. However, it is possible that, instead of being in a continuum state, the electron might be bound by the Coulomb field of the 3He nucleus. For more details see (1993HA1U, 2004AK06, 2004AK16, 2005AK04) and references therein.
The ratio of the axial-vector to the vector weak interaction coupling constants, GA/GV, can be obtained from half-life measurements. Fig. 1 in reference (2004AK06) shows a historical summary of values obtained for this ratio along with the value obtained by these authors, GA/GV = -1.2646 ± 0.0035. See also (2005AK04) where the same GA/GV ratio is obtained along with the comparative half-life value ft = 1129.6 ± 3.0 s which gives log ft = 3.053 ± 0.001. This ft value is used in (2009GA23) along with binding energies of 3H and 3He, to determine values for low energy constants in the chiral perturbation theory formulation of the NNN interaction.
| 2. 1H(6He, α)3H | Qm = 7.5093 |
With the advent of 6He beams in the 1990s, it became possible to study two-neutron transfer reactions (6He, α) with select targets, including 1H. Mostly such experiments were done with the intent of studying the cluster structure of 6He; see (2005GI07), for example. However, by observing the outgoing α spectrum, it becomes possible to study possible structure in 3H using this reaction. Two such studies have been reported: E(6He) = 19.3 MeV (1994AL54) and E(6He) = 23.9 MeV (2003RO13). The authors of (1994AL54) reported a peak in the α spectrum corresponding to the 3H ground state and a resonance-like structure that would correspond to a 3H state at 7.0 ± 0.3 MeV excitation energy with a width of 0.6 ± 0.3 MeV. The authors of (1994AL54) suggest that this 3H state might be a proton plus di-neutron system in analogy to 6He being an α plus di-neutron system. A theoretical study of such a model was reported in (1995BB09), in which it was suggested that the observed 3H state at 7 MeV is a 1/2+ state. In a similar experiment reported in (2003RO13), a resonance-like peak was observed at about 6.8 MeV excitation energy in 3H with a width no larger than 1 MeV. Since 3H has a neutron separation energy of 6.25 MeV, such a resonance would be about 0.8 MeV above the neutron-deuteron separation threshold. Thus, it would likely be observed in n-d scattering, but no such resonance has been seen. The authors of (2003RO13) suggest that the observed structure in the α spectrum might be a di-neutron state of 3H or that it might be due to three-body final state effects.
It was also reported in (1994AL54) that the reaction 1H(6Li, α)3He was studied with E(6Li) = 30 MeV. A peak corresponding to the ground state of 3He was observed, but there was no higher-lying peak analogous to the peak seen in this reaction.
A theoretical study of excited states in 3H and 3He is reported in (1999CS02).
| 3. 2H(n, γ)3H | Qm = 6.2572 |
An early review of experimental and theoretical aspects of this reaction can be found in (1981SH25). 
3.1 (in PDF or PS) in (1987TI07) lists pre-1987 references for this reaction. 
3.1 (in PDF or
PS) in this publication lists references since 1987. A compilation of neutron capture reactions throughout the periodic table is given in (2006MUZX). The value of the cross section for thermal neutron capture by 2H as recommended in (2006MUZX) is σ(Ethermal, γ) = 0.508 ± 0.015 mb. See also (2011FI11) which contains a list of measurements of the cross section for neutron capture by 2H and which gives an adopted value of 0.549 ± 0.010 mb. Cross sections for 2H(n, γ)3H and 3H(γ, n)2H are related by detailed balance, as is illustrated in (1986MI17). See also 3H reaction 8.
The importance of this reaction in astrophysical studies has been discussed in (1998NA15, 2002NA32, 2006NA25).
It is interesting to compare the cross sections for thermal neutron capture by 1H and 2H, as done in (2008PA37). As reported in (2006MUZX), these cross sections are 332.6 ± 0.7 mb and 0.508 ± 0.015 mb, respectively. Capture of thermal s-wave neutrons by both nuclei proceeds primarily by M1 transitions. Because of the orthogonality of the radial component of the scattering state in the 2H + n system with the dominant S component of the 3H ground state, neutron capture takes place through the small S' component of the 3H ground state which results in the small capture cross section value. In contrast, for the 1H + n system, as shown in (2008PA37), the radial parts of the scattering 1H + n state and the 2H ground state are essentially identical which results in a large capture cross section. See section IX.C.1 of (1998CA29) for a discussion of this point with relevant references.
Meson exchange currents (MEC's) play a significant role in the theory of neutron capture by light nuclei; see (1990FR19), for example. Indeed, MEC's were introduced by Riska and Brown (1972RI02) to explain the 10% difference between the calculated and experimental cross sections for the reaction 1H(n, γ)2H. A modern calculation demonstrating this can be found in (2005MA54). The effect of including MEC's is even more dramatic in the reaction 2H(n, γ)3H. Table II in (1983TO12) shows that the capture cross section is approximately doubled when MEC's are included. Essentially the same result is shown in Table IV in (2005MA54) using more modern interactions. In the reaction 2H(n, γ)3H at low energies where only s-waves need be considered, there are two channels to consider: 1/2+ and 3/2+. It is shown in (1983TO12, 1988KO07, 2005MA54) that the MEC's have their major effect in the 1/2+ channel and a relatively small effect in the 3/2+ channel.
Because of the Coulomb interaction, the mechanism for low energy proton capture 2H(p, γ)3He is different from that of the low energy neutron capture 2H(n, γ)3H. See 3He reaction 3 for more details.
Capture cross sections have also been measured for En = 30.5, 54.2 and 531 keV and astrophysical aspects discussed in (1998NA15, 2006NA25). As reported in (1986MI17) and (1987TI07), neutron capture cross sections have also been measured for En = 6.85 - 14 MeV. The data in (1986MI17) are analyzed by assuming that capture at these energies occurs by E1 and E2 transitions although anomalies are found in forward-backward asymmetry values when compared to proton capture by 2H which may be due to a larger than expected E2 component in the capture cross section. As shown in (1986MI17), cross section data are consistent with comparable photodisintegration measurements.
Calculations of capture cross sections using effective field theory for En = 20 - 200 keV are reported in (2005SA28). This reference also contains a short history of the study of n + d radiative capture with references. See also (2006SA1N). Additional calculations of the reaction 2H(n, γ)3H are reported in (2001SC16). It is pointed out in both (2005MA54) and (2006NA25) that calculated values of the n + d capture cross sections exceed the experimental values by about 10%. The reason for the difference is uncertain, but may have to do with Δ excitation currents.
Parity violation in polarized neutron capture is reviewed in (1994KR20).
See also 3H reaction 8 and 3He reaction 3.
| 4. 2H(n, n)2H |
Earlier references relating to this reaction are given in Tables 2.3.1a, b, c in (1975FI08) and 
3.3 (in PDF or
PS) and 
3.4 (in PDF or
PS) in (1987TI07). References since 1987 or not included in (1987TI07) are given in 
3.2 (in PDF or
PS).
Important parameters for describing low energy n + d scattering are the doublet and quartet scattering lengths, 2and and 4and. Frequently quoted experimental values are 2and = 0.65 ± 0.04 fm and 4and = 6.35 ± 0.02 fm; see (1971DI15, 1987TI07, 2003WI08). A related quantity is the coherent scattering length, bnd. See Eq. (1) in (2003BL07) or Eq. (8) in (2003WI08) for the relationship between these quantities. A measurement of bnd = 6.6649 ± 0.0040 fm has been reported in (2003BL07, 2003SC12) using neutron interferometry techniques. These reference also gives a world average of measured values of this quantity as bnd = 6.6683 ± 0.0030 fm. See also (2006HU16).
It has been known for many years that calculated values of 2and are correlated with calculated values of the 3H binding energy. This nearly straight line correlation is known as the Phillips line; see (2003WI08) for references. Using the Faddeev approach with a variety of NN and NNN interactions, a number of calculated values of 2and, 4and, bnd and the 3H binding energy are reported in Table I of (2003WI08). A striking feature of this table is that, although the values of 2and and the binding energy values have considerable scatter, 4and is nearly constant at around 6.34 fm. A similar observation is discussed in (2003SC12). In this reference, an average calculated value of 4and = 6.346 ± 0.007 fm was used together with their measured value of bnd = 6.6649 ± 0.0040 fm to deduce the value 2and = 0.645 ± 0.003 (exp.) ± 0.007 (theor.) fm. This value of 2and was used as an input parameter to calculate the binding energy of 3H using effective field theory; see (2006PL09). This value of 2and was also used in (2010KI05) in their study of various NNN interactions. There is a proposed experiment reported in (2004VA13) for which it is expected that a measurement of 2and with improved accuracy will be achieved. See also (2007VAZW). A study of 2and and 4and using Faddeev methods and several interaction models is reported in (1991CH16). Agreement between theory and experiment is reasonably good. The corresponding calculated values for the p-d scattering lengths 2apd and 4apd also reported in (1991CH16) differed significantly from the experimental values. For more details, see 3He reaction 7.
A common method for describing low energy elastic scattering is effective range theory in which the quantity kcot(δ(E)) is expressed in terms of the scattering length and a few other parameters. Here, k is the wave number in the center of mass system and δ(E) is the scattering phase shift. Effective range studies of doublet n-d scattering are reported in (2000BB05, 2006OR03) and references therein. Figs. 1 and 2 in (2006OR03) and the figure in (2000BB05) show experimental values of the quantity kcot(δ(E)) and graphs of parameterizations and theoretically derived curves. Emerging from such studies as these is the notion of a virtual doublet state in 3H at an energy of about -0.48 MeV; see Fig. 4 in (2006OR03), with 2and = 0.65 fm. An early discussion of such a state is given in (1979GI1F). Also emerging from effective range studies are values of asymptotic normalization parameters (ANP's). Values of ANP's for the 3H ground state and the virtual 3H state are obtained in (2000BB05).
3.2 (in PDF or PS) indicates that most measurements of this reaction since the previous evaluation have made use of polarized neutron beams. Such beams have enabled detailed measurements to be made not only of the differential cross section but also of the analyzing power, Ay, as functions of the scattering angle. As NN, NNN interactions and three-body calculations have gotten more sophisticated, it was discovered that the three-body models gave differential cross sections in good agreement with experiment, but resulted in a serious discrepancy between the calculated and experimental values of the analyzing powers. This effect has become known as the Ay puzzle or as the analyzing power puzzle. The analyzing power puzzle also shows up in p + d scattering both as a discrepancy in Ay for polarized protons and in the VAP iT11 for polarized deuterons and in p + 3He scattering. See 3He reaction 7 and (2006FI06) and references therein. The reference (1996GL05) contains a number of examples of the effect for both n + d and p + d scattering, as does (1998TO07). The reference (2007MI26) contains a discussion of the puzzle and of some attempts to explain its origin. These authors also study relativistic effects that may play a role in the explaining the puzzle. In reference (2003NE01), it is shown that the difference between the calculated and measured Ay values is essentially independent of the incident neutron energy for En = 2 - 16 MeV. Calculations reported in (2001CA44) show that the discrepancy has disappeared when En reaches 30 MeV. See (2008TO12) for more on the energy dependence of the Ay puzzle. These authors attribute the puzzle as being due to a new type of NNN interaction. Higher orders of chiral perturbation theory provide NNN interactions that may provide a solution to the Ay puzzle; see (2002EP03, 2006EP01). However, in a recent calculation using the hyperspherical harmonic method with the next-to-next-to leading order NNN interaction, the Ay puzzle is still evident; see (2009MA53) and references therein. See (2008TO20) for a discussion of the history of the analyzing power puzzle. See 3He reaction 7 for more on the analyzing power puzzle in the context of proton-deuteron scattering.
Additional studies of relativistic effects in n + d scattering are reported in (2005WI13, 2008WI02). Firstly, in (2005WI13), n + d differential cross sections and analyzing powers were calculated for En = 28, 65, 135 and 250 MeV. It was found that relativistic effects were of increasing importance as the energy increased and were seen mostly in the differential cross sections for angles larger than 160 degrees. Relativistic effects on the analyzing powers were found to be small. Secondly, in (2008WI02), calculations are reported of Ay values for n + d scattering for several neutron energies ≤ 65 MeV. The relativistic effect of primary interest in this study was the Wigner spin rotations. It was found that the effect on Ay became larger as the En decreased. The net result is that by including the Wigner rotations the Ay discrepancy is increased compared to the nonrelativistic calculations. The authors observe that this effect is due to the sensitivity of Ay to changes in the 3Pj components of the NN interaction. On this same point, see (1998TO07, 2008DO06).
| 5. | (a) 2H(n, p)nn | Qm = -2.2246 | |
| (b) 2H(n, nn)1H | Qm = -2.2246 |
Table 2.4.1 in (1975FI08) and 
3.5 (in PDF or
PS) in (1987TI07) give extensive lists of references of studies of deuteron breakup by neutrons. 
3.3 (in PDF or
PS) gives references for these reactions since 1987. For details about the analogous process of deuteron breakup by protons see 3He reaction 6.
In (1996GL05), Fig. 32 gives the total n + d breakup cross section as a function of the lab energy of the neutron. The quoted experiments are from the 1960s and 70s. The cross section rises from zero at threshold (En(lab) = 3.3 MeV) to about 175 mb at 18 MeV and declines to 100 mb at E(lab) = 60 MeV and continues to fall, according to calculations. Faddeev calculations with realistic NN interactions give a fairly good description of the total breakup cross section.
In kinematically complete three-body breakup experiments in which the two neutrons are observed, a commonly used way of viewing the coincidence spectrum of the two neutrons makes use of a three-body kinematical curve. If the observed neutrons are arbitrarily labeled n1 and n2, then the energy and emission angle of the unobserved proton can be determined from energy and momentum conservation if the neutron energies E1 and E2 , their polar angles θ1 and θ2 and the relative azimuthal angle φ12 are measured. For any given set of values of the laboratory angles θ1, θ2 and φ12 - determined by the locations of the detectors - the allowed values of E1 and E2 lie along a curve in E1-E2 space calculated using energy conservation. This curve is called the three-body kinematical curve; the arc length along this curve is called S and has units of energy. S is set equal to zero where E2 equals zero. Any pair of (E1, E2) values for coincidence neutrons corresponds to a point in this space on or near the kinematical curve. By dividing the S curve into bins, one can obtain differential cross sections d5σ/dΩ1dΩ2dS as functions of S. Several such curves can be seen in (2005SE05), for example, for different values of θ1, θ2 and φ12.
Some detector configurations have received special attention. They are referred to as collinear, coplanar-star, space-star, FSI (final state interaction) and QFS (quasifree scattering) configurations. If the angle φ12 is set to 180° (thus detecting neutrons scattered in opposite directions) and θ1 and θ2 are both set to 60°, then when E1 = E2, the proton will be at rest in the center of mass system. This point in E1-E2 space is called the collinear point. Since the neutrons are identical and the scattering angles are equal, the differential cross section will be symmetrical around the collinear point. For other values of θ1 and θ2 with φ12 = 180°, there will also be points at which the proton is at rest. However, the differential cross sections are not symmetrical around the collinear point in those cases. Such configurations which allow for the possibility of the proton being at rest in the center of mass system are called collinearity configurations. Examples are shown in (2005SE05) where differential cross sections are shown as functions of the arc length S and the collinearity points are labeled. See also Fig. 40 in (1996GL05).
The star configurations are ones in which the three nucleons, in the center of mass system, are emitted with equal momenta separated by 120°; thus the three momentum vectors form an equilateral triangle. Any configuration allowing for this condition to occur at some point on the S curve is called a star configuration. The plane containing the equilateral momentum triangle is called the star plane. By a suitable arrangement of detectors, this plane can have any orientation, but two orientations are of particular interest. When the star plane lies in the same plane as the beam, the configuration is referred to as a coplanar-star configuration. When the star plane is perpendicular to the beam, the configuration is called the space-star configuration. Differential cross sections for each of these configurations can be seen in (2005SE05), for example. This reference also contains a histogram in E1-E2 space, Fig. 8, for the space-star configuration.
The QFS configuration allows for one of the three nucleons in the final state to remain at rest in the lab system, as if it were a spectator to the scattering process. See (2002SI06) for an example in which three-body breakup is used to study n + p and n + n scattering.
The FSI configuration allows for two nucleons to be emitted with approximately equal momenta and only a small relative momentum. In this case, the interaction of the two co-moving nucleons will be emphasized. In n + d breakup reactions, this configuration has made the study of the interaction of two neutrons possible. See (2000HU11) and (2001HU01) as examples of where studies using the FSI configuration are reported.
In connection with the space-star configuration, it has been found that the calculated differential cross section using realistic NN and NNN interactions is in disagreement with experimental results. This discrepancy is called the space-star anomaly. See (1988ST15, 1989ST15, 1996SE14, 1998HO08, 2001ZH09, 2005SE05). The origin of this anomaly isn't completely understood, but the authors of (2005SE05) suggest that some aspect of the three-body force may still be missing in the calculations.
Kinematically complete neutron-deuteron breakup reactions have been used to measure the neutron-neutron scattering length, ann; see (1996WI22) for a theoretical discussion of such reactions. Experiments were performed at two laboratories to obtain ann; see (2001HU01, 2006GO11) and references therein. The resulting values of ann obtained from the two laboratories were inconsistent. The reason for the inconsistency remains unclear. See (2009GA1D) for an extensive discussion of these matters.
| 6. 2H(p, π+)3H | Qm = -134.0953 |
References for this reaction are listed in 
3.4 (in PDF or
PS). This reaction is often studied in conjunction with the reaction 2H(p, π0)3He. See 3He reaction 5 for additional discussion. There are no reports of the reaction 1H(d, π+)3H where the target and projectile are reversed.
| 7. 3H(γ, π-)3He | Qm = -139.5516 |
There are four pion photoproduction reactions relating 3H and 3He, namely 3H(γ, π-)3He, 3He(γ, π+)3H, 3H(γ, π0)3H and 3He(γ, π0)3He. References for the first of these are listed here. References for the second are listed in 3He reaction 9. References for the third and fourth are listed in 3He reaction 8.
Only two references for this reaction have appeared since the previous evaluation (1987TI07). For Eγ = 250 - 450 MeV, studies of the two reactions 3H(γ, π-)3He and 3He(γ, π+)3H were reported in (1987BE27). They measured the differential cross section for a range of energies and for several different values of the square of the momentum transfer. Comparison with theory showed poor agreement. Another paper by the same group (1988BE61) shows some new data for this reaction as well as the data from reference (1987BE27) in the context of the development of a solid state detector.
Calculations of polarization observables in the photoproduction of π- particles from 3H (and from 13C and 15N, as well) are reported in (1993CH26).
| 8. | (a) 3H(γ, n)2H | Qm = -6.2572 | |
| (b) 3H(γ, d)n | Qm = -6.2572 | ||
| (c) 3H(γ, p)2n | Qm = -8.4818 | ||
| (d) 3H(γ, 2n)1H | Qm = -8.4818 |
Reactions (a) and (b) are two-body photodisintegration reactions listed separately to indicate which outgoing particle is observed, the neutron in (a) and the deuteron in (b). Similarly, reactions (c) and (d) are three-body photodisintegration reactions in which either the proton or the two neutrons are observed .
There are no reports of measurements related to reactions (a), (b), (c) or (d) since the previous evaluation.
In the past, experimental and theoretical studies of the photodisintegration of 3H have often been carried out in conjunction with the photodisintegration of 3He and of neutron and proton capture by 2H. Hence, 3H reaction 3 and 3He reactions 3 and 10 should be consulted for additional information regarding these processes.
A few measurements of reactions (a) and (c) are reviewed in (1975FI08). Also, reference (1981FA03) contains a summary of the experimental results up to 1981 for the photoneutron reactions (a) and (d). Figs. 10, 11 and 13 of that reference show cross sections for reactions (a) and (d) and their sum for Eγ from threshold to about 28 MeV. For the two-body disintegration, reaction (a), the cross section climbs rapidly from threshold, reaches its peak value of around 0.9 mb at about 12 MeV and drops slowly to around 0.2 mb at 26 MeV. The three-body disintegration, reaction (d), rises moderately rapidly from threshold to a peak value of around 0.9 mb at about 15 MeV and falls to about 0.4 mb at 26 MeV. As discussed in (1975GI01) and (1987LE04), for Eγ from threshold to around 40 MeV, two-body photodisintegration of 3H (or 3He) takes place by an E1 transition from the spatially symmetric component of the ground state to the p-wave state with a deuteron plus a neutron (or proton). The reference (1981FA03) also contains a useful overview of the theoretical work on the photodisintegration of 3H and 3He prior to 1981. A review of low energy photonuclear reactions on 3H and 3He is presented in (1987LE04).
A calculation of the photodisintegration of 3H (as well as 3He) using the Lorentz Integral Transform method with realistic NN and NNN interactions is reported in (2000EF03). For more on this approach, see the Introduction and reaction 10 in the 3He section. A theoretical study of reaction (d) and the analogous reaction 3He(γ, d)1H using the Faddeev approach with modern interactions is reported in (2003SK02). Comparisons are made with experimental results and references for the data are given. The role of 3N interactions is studied as are different approaches that include meson exchange currents. A similar study is reported in (1998SA14). In both of these studies, it is observed that there is a correlation between the peak heights of the photodisintegration cross section and the binding energy of 3H; see Fig. 9 in (1998SA14). A study of photonuclear reactions on 3H and 3He up to the pion threshold that includes Δ isobar excitation is presented in (2002YU02, 2004DE11).
Integrated moments for the reactions (a), (c) and 3He(γ, n) are quoted in (1981FA03, 1987TI07).
| 9. | (a) 3H(e, e)3H | ||
| (b) 3H(e, e'n)2H | Qm = -6.2572 | ||
| (c) 3H(e, e'p)2n | Qm = -8.4818 |
There are no reports of new measurements of reaction (a) since the previous evaluation. See below for a report of inclusive inelastic scattering of electrons by 3H.
A brief history of experimental studies of electron scattering by 3H and 3He is given in the Introduction section of (1994AM07). This reference summarizes results from three previous reports, namely (1982CA15, 1985JU01, 1992AM04). Of the three reports, only (1985JU01) deals with reaction (a), a discussion of which was included in the previous evaluation (1987TI07). The authors of (1994AM07) combined their data with the world data to obtain charge and magnetic form factors for 3H and 3He for q2 up to 30 fm-2 and compared with theory and with 2H and 4He form factors.
It has proven to be of value to study the charge and magnetic form factors, Fc and Fm, that can be obtained from the electron elastic scattering cross sections. See (1985JU01), for example, in the context of obtaining the form factors for 3H. These quantities are expressed as functions of q2, the square of the momentum transferred to the target in the scattering process. Two different units are used in the literature for q2, namely fm-2 and (GeV/c)2. The conversion factor is 1 (GeV/c)2 corresponds to 25.6 fm-2 or 1 fm-2 corresponds to 0.0391 (GeV/c)2. It should be noted that as a unit for q2, (GeV/c)2 is sometimes written as just (GeV)2, as in (2007PE21) and (2007AR1B). The form factors are defined in such a way that both Fc and Fm equal 1 at q2 equal to zero. Fig. 1 in (1985JU01) shows both form factors for 3H for q2 from 0 to about 23 fm-2 and 31 fm-2 for Fc and Fm respectively. The form factors drop rapidly with increasing q2 and each has a minimum at about 13 fm-2 for Fc and at about 23 fm-2 for Fm. Figs. 6 and 7 in (1994AM07) show the charge and magnetic form factors for both 3H and 3He. Similar graphs are shown in Figs. 6 - 9 in (2009LE1D). The 3He form factors are qualitatively similar to those for 3H; the minima occur at slightly different values of q2. Since 3H and 3He form an isospin doublet, it is useful to consider the isoscalar and isovector combinations of the form factors of 3H and 3He; see (1992AM04, 1994AM07) for the relationship between the standard form factors and the isoscalar and isovector form factors. As discussed in (1992AM04), meson exchange currents are expected to make a larger contribution to the isovector form factors than to the isoscalar ones. The isoscalar and isovector form factors are shown in Figs. 12 and 13 of (1994AM07).
Charge and magnetic rms radii values have been obtained from form factors; see (1988KI10), for example. This reference discusses the methods and difficulties in deducing rms radii values from form factors and quotes a range of values for the charge radii obtained for 3H and 3He. The slopes of the charge and magnetic form factor curves at q2 = 0 are related to the mean square radii; see Eq. (9) of (1988KI10), for example. Using data from earlier experiments, the charge and magnetic rms radii of 3H are obtained from slopes of form factor curves and reported in (1994AM07) to have the values rch = 1.755 ± 0.086 fm and rm = 1.840 ± 0.181 fm. The reference (1994AM07) also reported the corresponding values for 3He to be rch = 1.959 ± 0.030 fm and rm = 1.965 ± 0.153 fm.
A theoretical study of the correlation between the 3H binding energy and the charge radius is reported in (2006PL02), following an earlier calculation reported in (1985FR12). Averaging two calculations with different choices of input data, the authors obtained a charge radius of 2.1 ± 0.6 fm.
With regard to reactions (b) and (c), there have been no reports of any experiments since the previous evaluation.
There is a study of inclusive inelastic electron scattering from 3H (and 3He) for low excitation energies reported in (1994RE04). Longitudinal and transverse response functions were obtained for six values of the momentum transfer between 0.88 fm-1 and 2.87 fm-1 for excitation energies less than 18 MeV. The experimental results for the response functions were compared with values calculated using several different techniques. The agreement was better for smaller values of the momentum transfer and excitation energy than for larger values. It is observed that the longitudinal response function near threshold is somewhat larger for 3He than for 3H. This effect has been observed in earlier experiments and has been attributed to a Coulomb monopole transition; see references in (1994RE04). Inclusive inelastic electron scattering measurements for 3H and 3He are reported in (1988DO13). Longitudinal response functions were measured for momentum transfers from 200 MeV/c (1.0 fm-1) to 550 MeV/c (2.78 fm-1). (Note: Two different units are used for momentum transfer values, namely fm-1 and MeV/c. The conversions between the two are 100 MeV/c corresponds to 0.506 fm-1 and 1 fm-1 corresponds to 198 MeV/c.) Calculations of the longitudinal response function with the Lorentz Integral Transform method using realistic NN and NNN interactions and comparing theory with the experimental data of (1988DO13, 1994RE04) are reported in (2004EF01).
For more details on inclusive inelastic electron scattering in the quasi-elastic region for 3H and 3He, see 3He reaction 11.
| 10. | (a) 3H(π±, π±)3H | ||
| (b) 3H(π+, π0)3He | Qm = 4.6122 | ||
| (c) 3H(π+, γ)3He | Qm = 139.5888 |
With respect to reaction (a), the reference (2002BR49) is the last of a series of reports measuring elastic scattering of π+ and π- from 3H and 3He at Eπ = 142, 180, 220 and 256 MeV. A major focus of these studies is charge symmetry breaking (CSB). The accompanying theoretical report is (2002KU36); the earlier experimental reports are referenced in (2002BR49), in the charge symmetry review (1990MI1D) and in 3He reaction 13. See also (1999CO08) for an analysis of this data. The theory report (2002KU36) contains figures showing experimental and theoretical angular distributions for the four cases π+ + 3He, π+ + 3H, π- + 3He, π- + 3H at the four energies mentioned above. In each case, the diffraction pattern has a minimum at a scattering angle of about 80° and is fairly flat at larger angles. Ratios of cross section pairs were defined such that - if charge symmetry held - they would each equal unity at all angles and energies. Fig. 1 in (2002BR49) summarizes a number of experiments that measure these ratios. For each ratio and each energy, there are significant deviations from unity, especially near the 80° scattering angle. Corresponding figures in (2002KU36) compare calculations which take into account CSB effects with the data. Except for the 142 MeV data, the theoretical results agree well with the data.
One source of CSB between 3H and 3He is the repulsive charge of the protons in 3He compared to the neutrons in 3H. This effect leads to slightly different distributions and rms radii of the neutrons and protons in the two nuclei. The authors of (1991GI02) conclude that the neutron rms radius in 3He is larger than the proton radius in 3H by 0.035 ± 0.007 fm and that the rms proton radius in 3He is larger than the rms neutron radius in 3H by 0.030 ± 0.008 fm. This result was also discussed in (2002KU36, 2007KR1B) in a more general context of determining neutron and proton distributions using pion scattering.
For additional theoretical references related to reaction (a), see (1987KI24, 1989BR02, 1991BR33, 1995BR35, 1995CH04, 2001BR33).
The only report of a study of the charge exchange reaction (b) is (1995DO06) in which a 142 MeV π+ beam was used and the recoiling 3He nucleus was observed. The momentum distribution and differential cross section of the outgoing 3He nuclei were measured and compared to theory and previous measurements. Of interest in the experiment was the comparison of the spin-flip and the non-spin-flip contributions to the cross section.
There were no reports of reaction (c) for the time period of this evaluation.
| 11. | (a) Λ3H(π-)3He | Qm = 42.6936 | |
| (b) Λ3H(π-)2H1H | Qm = 37.2001 | ||
| (c) Λ3H(π-)1H1Hn | Qm = 34.9756 |
Studies of hypernuclei in general and the decay of the hypertriton in particular have been fruitful to both nuclear and particle physics. General references and reviews are listed below.
For completeness, some properties of the Λ and Σ hyperons are listed from the Particle Data Group publication. The Λ particle has zero charge, strangeness -1, isospin 0, Jπ = 1/2+, mass = 1115.683 ± 0.006 MeV and mean lifetime = (2.632 ± 0.020) × 10-10 s which corresponds to a decay width of about 2.50 × 10-6 eV. The major decay modes are (p + π-) at 64% with an energy release of about 38 MeV and (n + π0) at 36% with an energy release of 41 MeV.
Closely related to the Λ hyperons are the Σ hyperons with strangeness -1, isospin 1 and Jπ = 1/2+. The neutral member of the three Σ's is Σ0 with a mass of 1192.642 ± 0.024 MeV which is about 77 MeV more massive than the Λ. Its basic quark structure is the same as that of Λ. It decays almost 100% into Λ + γ. It has a mean lifetime of (7.4 ± 0.7) × 10-20 s, which corresponds to a decay width of about 8.9 keV.
In the early days of hypernuclear physics studies, the hypertriton was produced by capturing a stopped K- meson. For example, in (1973KE2A), the reaction 4He(K-, π-p)Λ3H was used to produce hypertritons. More recently, the reaction 3He(e, e'K+)Λ3H, with Ee = 3.245 GeV, has been used; see (2001RE09, 2001ZE06, 2004DO16). The reaction (π+, K+) with π+ energy of 1.05 GeV has been used to produced heavier hypernuclei; see (1996HA05, 1998BH05) and references therein.
No bound states of A = 2 hypernuclei, such as Λ2H, have ever been observed, nor have other A = 3 hypernuclei such as Λ3He. For A = 4 hypernuclei, two bound systems are known, namely Λ4H and Λ4He. It has been pointed out in (1989AF1A) and (1995GI16) that, as the lightest bound hypernucleus, the hypertriton plays a similar role in hypernuclear physics to that which the deuteron plays in ordinary nuclear physics. Analogous to the way in which the bound state properties of the deuteron are used to put constraints on models of the nucleon-nucleon interaction, the bound state properties of the hypertriton can be used to constrain the hyperon-nucleon interaction.
The hypertriton consists primarily of a weakly bound system of a deuteron and a Λ particle. Because of the strong coupling between the Λ and the Σ hyperons, the hypertriton has a small probability of being a deuteron and a Σ particle. A recent calculation gives that percentage as 0.15% and 0.23% for two different interactions that give approximately the current Λ binding energy; see (2002NE11). An earlier calculation (1973DA2A) gives the Σ component to be 0.36%. However, in the calculation reported in (1973DA2A), the 1/2+ state is more deeply bound than measurement gives and an unobserved bound 3/2+ state is predicted. A Faddeev calculation of the hypertriton using realistic interactions reported in (1995MI12, 1998GL01) gives 0.5% as the Σ component probability.
The hypertriton has Jπ = 1/2+, isospin 0 and the Λ separation energy = 0.13 ± 0.05 MeV; see Appendix IV in Nuclear Wallet Cards (2005TUZX) and (1995GI16) and references therein. A simplified model of the hypertriton as a deuteron plus Λ is discussed in (1992CO1A). The deuteron is treated as a free deuteron and a Λ-deuteron potential is developed. The experimental Λ separation energy is used as an input to calculate the Λ part of the hypertriton wave function. The resulting wave function is used to calculate the hypertriton lifetime and the branching ratio, R, defined below. The calculated results agree with experiment within experimental error, as will be discussed below.
In addition to the π- decay processes listed in reactions (a), (b) and (c), the corresponding π0 processes are also possible: Λ3H(π0)3H, Λ3H(π0)2Hn, Λ3H(π0)1Hnn. All of these π- and π0 processes are referred to as mesonic decay modes. In addition, the following non-mesonic decay modes are possible in principle: Λ3H → 2H + n and Λ3H → 1H + n + n.
The reference (1973KE2A) gives a measured value of (2.46+0.62-0.41) × 10-10 s for the lifetime of the hypertriton. This is the latest (1973) of several measurements. Table 1 in (1990CO1D) contains a list of measured values of lifetimes of light hypernuclei, including the hypertriton. Although the uncertainty in the measurement of the hypertriton lifetime is quite large, it appears that it is comparable to and possibly somewhat smaller than that of the free Λ particle. In the simplified model of the hypertriton in (1992CO1A) referred to above, the calculated value of this lifetime is 12% smaller than that of the free Λ. In the study reported in (1998KA12), the calculated value of the hypertriton lifetime is 3% larger than the free Λ lifetime. Since the hypertriton is primarily a loosely bound Λ state, it isn't surprising that its lifetime is comparable to the free Λ. In heavier hypernuclei where the Λ binding energy is greater, the measured and calculated lifetimes tend to be lower than the free Λ; see (1998BH05).
In hypernuclei heavier than the hypertriton, the major decay mode is the non-mesonic decay because the mesonic decay modes are suppressed by the Pauli principle. To see why this occurs, recall that when the Λ decays into a nucleon and a pion, the energy released is about 40 MeV. Most of this energy goes to the pion, leaving only a small amount of energy and momentum for the nucleon. However, in nuclei heavier than the triton most of the low energy and momentum states are full, thus inhibiting this decay mode. For example, in Λ12C the ratio of the π- decay rate to the non-mesonic decay rate is found experimentally to be 0.045 ± 0.04; see (1989GI10) and references therein. In the hypertriton, there are empty states available at low energy and the mesonic decay mode is the active decay mode. Using numbers from Table I in (1998KA12), the calculated value of this ratio for Λ3H is 15.2.
Reaction (a) is a two-body π- decay while (b) and (c) are three- and four-body π- decays. The branching ratio R = Γ(Λ3H → π- + 3He)/Γ(Λ3H → all π- modes) has been measured several times; Γ is the decay rate. Table 4 in (1992CO1A) collects the measured values (with references) and gives an average value for the ratio to be R = 0.35 ± 0.04. In the simplified model of the hypertriton in (1992CO1A) referred to above, the calculated value of this ratio is R = 0.33 ± 0.02, where the theoretical uncertainty results from an uncertainty in a parameter of the model. Using numbers from Table I in (1998KA12), the calculated value of this ratio for Λ3H is R = 0.379; see also (1998GL01).
In studies of the decay of hyperons and hypernuclei, an empirical observation called the ΔI = 1/2 rule has received considerable attention. This rule can be illustrated in the two-body mesonic decay of Λ3H, reaction (a). Before decay, the isospin is zero for the Λ and zero for the deuteron. After decay into an isospin 1/2 triton and an isospin 1 pion, the final isospin could be either 1/2 or 3/2. Thus the change in isospin in the decay process is either 1/2 or 3/2. In (1989GI10), it is reported that, experimentally, "...one finds the ΔI = 1/2 amplitude to be enhanced by an order of magnitude over the ΔI = 3/2 amplitude." See (1989GI10) for a discussion of the ΔI = 1/2 rule, including examples and references. This rule was used explicitly in (1998KA12) in the calculation of the decay rates of the hypertriton. See also (2000AL27) for a study of the ΔI = 1/2 rule in hypernuclei. See also (2005SA16) for a possible violation of the ΔI = 1/2 rule in hypernuclei.
Additional theoretical studies of the hypertriton can be found in (1989AF1A, 1990AF02, 1992BE02, 1993MI21, 1995DO01, 1995MI06, 1995MI12, 1997GO04, 1998BL17, 1998GL10, 1998GO06, 1999GO19). General reviews of hypernuclear physics can be found at (1989GA15, 1995GI16) and various measurements in Nuclear Physics A 639 (1998) which result from the 1997 Symposium on Hypernuclear and Strange Particle Physics.