Two-nucleon Transition Research Articles

Pion absorption from the lowest atomic orbital in 2H, 3H and 3He

Abstract. The π− + 2H → n + n, π− + 3H → n + n + n, π− + 3He → n + d and π− + 3He → p + n + n capture reactions from the lowest atomic orbitals are investigated under full inclusion of final state interactions and employing the single-nucleon and two-nucleon transition operators derived at leading order in chiral effective field theory.

Pion absorption from the lowest atomic orbital in H2, H3 , and He3

The ${\ensuremath{\pi}}^{\ensuremath{-}}+^{2}\mathrm{H}\ensuremath{\rightarrow}n+n, {\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{H}\ensuremath{\rightarrow}n+n+n, {\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}n+d$, and ${\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}p+n+n$ capture reactions from the lowest $1S$ atomic orbitals are studied under full inclusion of final state interactions. Our results are obtained with the single-nucleon and two-nucleon transition operators derived at leading order in chiral effective field theory. The initial and final three-nucleon states are calculated with the chiral nucleon-nucleon semilocal momentum space potential up to ${\mathrm{N}}^{4}{\mathrm{LO}}^{+}$, augmented by the consistently regularized chiral ${\mathrm{N}}^{2}\mathrm{LO}$ three-nucleon potential. We found that absorption rates depend strongly on the nuclear pion absorption operator used, and its two-body parts change the rates by a few orders of magnitude. The final state interactions between nucleons generated by the two-nucleon forces are also important, while the three-nucleon interaction plays a visible role only in the ${\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}n+d$ reaction. Our absorption rate for the ${\ensuremath{\pi}}^{\ensuremath{-}}+^{2}\mathrm{H}\ensuremath{\rightarrow}n+n$ process is in good agreement with the experimental data from the hadronic ground-state broadening in pionic deuterium. The capture rates on $^{3}\mathrm{He}$ are also generally consistent with the spectroscopic data within error bars, though our central values are found to be systematically below the data. We show that for the three-body breakup processes the dominant contributions to the absorption rates arise from the quasi-free scattering and final-state interaction kinematical configurations.

The Inverse-Scattering Problem: The View of a Few-Nucleon Theorist

The theoretical step from the experimental phase shifts in the partial waves of the nuclear force to a parametrization of the two-nucleon interaction is discussed. A nuclear-physics solution to the inverse-scattering problem is recalled. The procedure is only based on the assumption of Hermiticity for the underlying potential. The procedure is provided by the off-energy-shell continuation of the two-nucleon transition matrix. It is compared with the strategies of mathematicians for the same problem. Faddeev strongly influenced the mathematical side of the problem.

Orthogonal polynomial approach to calculate the two-nucleon transition operator in three dimensions

We give a short report on the possibility to use orthogonal polynomials (OP) in calculations that involve the two-nucleon (2N) transition operator. The presented work adds another approach to the set of previously developed methods (described in Phys. Rev. C 81, 034006 (2010); Few-Body Syst. 53, 237 (2012); K. Topolnicki, PhD thesis, Jagiellonian University (2014)) and is applied to the transition operator calculated at laboratory kinetic energy 300MeV. The new results for neutron-neutron and neutron-proton scattering observables converge to the results presented in Few-Body Syst. 53, 237 (2012) and to results obtained using the Arnoldi algorithm (Y. Saad, Iterative methods for sparse linear systems (SIAM Philadelphia, PA, USA 2003)). The numerical cost of the calculations performed using the new scheme is large and the new method can serve only as a backup to cross-check the previously used calculation schemes.

Transfer strengths to the0+states excited by (p,t) reactions inBa130,132,134

The aim of this work is to calculate the transfer strengths to the excited ${0}^{+}$ states in $^{130,132,134}\mathrm{Ba}$ which have been identified in ($p,t$) reactions and to investigate their related properties. For this purpose, we have used a model Hamiltonian which includes monopole pairing, quadrupole-quadrupole, and spin-quadrupole interactions. The model Hamiltonian has been diagonalized with the random phase approximation (RPA). To investigate the general trend of the transfer strengths to the excited ${0}^{+}$ states, two-nucleon transition intensities relative to the transition to the ground state and their cumulative values have been calculated versus energy and compared with the data. The comparisons revealed that fairly good results for the distribution of the energies and the transfer strengths have been obtained. For almost all nuclei, the cumulative values of the transfer strengths were nicely predicted. Moreover, qualitatively, a parallel result that agrees with the data and the prediction of the O(6) limit of the IBM model which is a weak excitation for the first ${0}^{+}$ state and a strong one for the second ${0}^{+}$ state has been obtained for $^{130}\mathrm{Ba}$ and $^{132}\mathrm{Ba}$.

Reaction spectroscopy at fragmentation beam energies – recent advances in studies of two-nucleon removal

Final-state-exclusive two-nucleon removal reaction data from fast fragmentation beams can provide a demanding test of the microscopic two-nucleon transition densities calculated from large-basis shell model wave functions. The sensitivity of measured partial cross sections to pairing and other correlations is discussed. It is also suggested that the widths of the momentum distributions of these partial cross sections will exhibit a strong dependence on the final-state of the residue and the projectile structure.

Effects of final-state interaction in inelastic electron scattering from the three-nucleon system

Inclusive electron scattering from 3He is microscopically described. The calculation assumes nucleonic degrees of freedom only for the three-nucleon states. The nucleons interact among each other through realistic two-nucleon potentials. They interact with the electron through one-nucleon electromagnetic currents. Compared to the standard plane-wave impulse approximation the theoretical description of the final three-nucleon scattering states is improved. A perturbative approach is used. Final-state interaction is approximately accounted for by one additional rescattering in terms of the two-nucleon transition matrix. The final three-nucleon scattering states are fully antisymmetrized.

Elastic scattering and break-up processes in then-d system

A method to solve the AGS equations in momentum space is presented. The two-nucleon transition operators are generated with the new Bonn potential restricted to the states1S0,3S1-3D1,3P0,1P1,3P1,3P2-3F2,1D2 and3D2. Cross sections and analyzing powers for elastic and break-up processes are calculated at a neutron laboratory energyEn=10.3 MeV.

A microscopic model analysis of the 90Zr(p, n) IAS transition

Direct reaction (p, n) data to the isobaric analogue of the ground state of 90Zr is analysed within a DWA using a complex effective two-nucleon transition interaction, the real part of which has been used in many previous inelastic scattering analyses. Using collective model form factors in the ansatz for the imaginary part of the transition interaction and allowing for virtual resonance excitation, the differential cross sections from the scattering of 18.5–45 MeV protons are well reproduced. The parameters of the required complex interaction have a smooth energy variation similar to that required by a microscopic model analysis of proton inelastic scattering to collective states in nuclei.

Ratio of in zirconium isotopes

The modified random phase approximation is applied for studying pairing vibrations in Zr isotopes. The ratio of [Formula: see text], which is related to the ratio of the square of the two-nucleon transition amplitude, is calculated for different zirconium isotopes and compared with the experimental result.

Off-energy-shell variations of two-nucleon transition matrix and three-nucleon problem

For a schematic three-nucleon problem, we derive approximate analytic expressions for the functional derivatives of measurable three-particle quantities with respect to off-shell variations of the triplet-s, two-nucleon transition matrix. Those quantities include neutron-deuteron scattering lengths, trinucleon binding energies, and the 3He charge form-factor minimum; correlations between off-shell changes in the latter two are discussed. We indicate how results of this kind may be used to decide whether or not a given set of discrepancies between calculated and experimental three-nucleon observables can be reconciled in terms of off-shell variations of a nonretarded hermitean two-nucleon interaction. The treatment is not restricted to special classes of phase-shift equivalent potentials or phase-shift preserving transformations but instead makes use of a systematic parameterization of off-shell variations in terms of symmetric rational approximants of increasing order.

Explicit time-reversal violating interactions for nuclear physics

Starting from a T-violating Lagrangian involving the nucleon, meson and electro magnetic fields interacting at a point, we calculate the one meson exchange diagram and obtain the longest range part of a two-nucleon electromagnetic operator. The cases when the meson is scalar, pseudoscalar and vector are considered. For the radiation of a real photon the multipole expansions of the transition operators are obtained. The properties and expected magnitudes of the resulting explicit two-nucleon transition operators are examined and compared to the normal operators. With the interactions at ‘maximal’ strength any contributions from the vector operators are negligible and violations from the other operators are only likely to reach the order of 10 −3 where the normal transitions are strongly inhibited. When the photon is virtual the interactions lead to explicit T-violating three-nucleon potentials. These potentials give practically no contributions to optical model potentials. The best reciprocity experiments appear to be nucleon transfer reactions, and there could be violations of the order of 10 −3 in ( d − p) reactions from the pseudoscalar potential. This potential is shown to give a stripping amplitude with angular properties very different from the normal one.

The generator coordinate method applied to pairing vibrations

The generator coordinate integral equation is solved for the pairing Hamiltonian with the gap parameter Δ as the generator coordinate. This is shown to be a poor approximation in the weak pairing limit, so an improved wave function is used. Applications are made to the pairing vibrational spectra and two-nucleon transition strengths in 206,208,210Pb and the single-particle levels in 207,209Pb.

Off-energy-shell continuation of the two-nucleon transition matrix in the presence of tensor forces

Abstract For a coupled partial wave with a bound state, the entire T-matrix is determined by the bound-state energy and wave function, the on-shell mixing parameter and a real symmetric matrix function σ(k2,α2 k1α1) of the continuous momentum variables k and the discrete eigenchannel labels α. The on-shell part of σ is given by the eigenphases, the arbitrariness of the T-matrix is the off-shell continuation of this phase-shift matrix σ(kα2, kα1) into two dimensions. Three possible techniques are suggested to go from α to the entire T-matrix. This construction procedure for T avoids the usual complications of a potential fit.

Off-Shell Continuation of the Two-Nucleon Transition Matrix with a Bound State

A method of continuing the two-nucleon transition matrix off the energy shell for bound-state, partial-wave eigenchannels is presented. The arbitrary parmeters of this method are a symmetric function of momentum ${\ensuremath{\sigma}}_{W}(k,{k}^{\ensuremath{'}})$ and the bound-state wave function ${\ensuremath{\Psi}}_{B}(r)$. The phase-shifts are essentially contained in ${\ensuremath{\sigma}}_{W}(k,k)$. While a potential is presumed to be present, it never explicitly appears in determining the $T$ matrix.

Off-energy-shell continuation of the two-nucleon transition matrix

For an uncoupled partial wave without bound state, the symmetric part σ ( k, k′) of the half-shell T-matrix can be given arbitrarily. This in turn determines the entire T-matrix. Since σ( k, k) is essentially the phase shift, the arbitrary part of T appears as a continuation into two dimensions of the phase shift function, symmetry being the only restriction. This formulation stays closer to experiment than the usual one, in which the arbitrary function is the potential V( k, k′). A practical method is given to go from σ to the entire T-matrix.