Photodisintegration of 4He and the Supermultiplet Potential Model of Cluster-Cluster Interactions

p+³H and p+³He elastic collisions are described in terms of a supermultiplet model with [ƒ]-dependent potentials. The phase shifts δ ^[ƒ] _L,t,S (E) with [ƒ] = [4], t = S = 0, L = even are reconstructed from the observable nuclear phase shifts δ _L,S (E) of the above collisions. So, the initial-state interaction V ^[4] _L,0,0 (R) of the ⁴He +Υ→³H +p(³He +n) reaction can be found unambiguously, while the final-state interaction V ^[31] _{L, 1, 0} (R) is defined by the observablesδ _L,0 (E) of p+³He scattering. The data on the proton momentum distribution in ⁴He and on the charge-exchange reaction ³H +p→³He +n confirm the model. In calculating the above photonuclear reactions, in addition to the initial-state and final-state antisymmetrizations, preserving the corresponding symmetry [ƒ], the nucleon-nucleon correlations in the ³H (³He) subsystem were also taken into account. The results are in good agreement both with recent experimental data and theoretical investigations by sofianos, Fiedeldey, and Sandhas, who followed a rather different approach. Received August 5, 1994; revised November 30, 1994; accepted for publication December 30, 1994     

Quasifree processes in the 2H + 3He interaction

Quasifree scattering and quasifree reaction processes have been examined in the ³He+ ²H → p+d+d, ³He + ²H → n+p+³He and ³He+²H → p+p+t reactions. Beam energies of E_d = 22.3 and 35 MeV and of E_3He = 30, 33.5, and 52.5 MeV were used. The experimental results are compared with PWIA calculations and Fourier transforms of the wave functions are extracted. The quasifree processes are described qualitatively by the PWIA, but some features cannot be described by either PWIA or DWIA.     

Odd-even features in 3He + 3H scattering

The single-channel resonating-group method is used to study effects of the Pauli principle on ³He + ³H scattering. Comparison is made with previous similar calculations for d + ³He scattering, and it is found that the Pauli principle affects the s = 0 state of the ³He + ³H system rather similarly to the way it affects the s = 1 state, whereas the Pauli principle affects the $\text{s =}\text{3}\text{2}$ state of the d + ³He system quite differently from the way it affects the $\text{s =}\text{1}\text{2}$ state. Mention is made of the possibility of observing similar effects of the Pauli principle in other nuclear systems.     

Antisymmetry and channel coupling contributions to the absorption for p+αd+3He

To understand recently established empirical p+α potentials, RGM calculations followed by inversion are made to study contributions of the d+³He reaction channels and deuteron distortion effects to the p+α potential. An equivalent study of the d+³He potential is also presented. The contributions of exchange non-locality to the absorption are simulated by including an phenomenological imaginary potential in the RGM. These effects alone strongly influence the shape of the imaginary potentials for both p+α and d+³He. The potentials local-equivalent to the fully antisymmetrised-coupled channels calculations have a significant parity-dependence in both real and imaginary components, which for p+α is qualitatively similar to that found empirically. The effects on the potentials of the further inclusion of deuteron distortion are also presented. The inclusion of a spin-orbit term in the RGM, adds additional terms to the phase-equivalent potential, most notably the comparatively large imaginary spin-orbit term found empirically.     

N1−3H configurations in 4He

Wavefunctions for N¹?³H configurations in ⁴He are calculated using NN → N¹N transition potentials V and ³HN → N¹³H transition potentials from a two-nucleon exchange mechanism. The radial N¹?³H momentum distributions peak at ～ fm^?1 which is much lower than the short-ranged V. For (πN) S-wave isobars, e.g. N¹(1535) and N¹(1700), N¹?³H probabilities are estimated to be ～2‰ each, while those for N¹'s in higher (πN) partial waves are much smaller.     

Cross section of the <Superscript>3</Superscript>H(d, <Superscript>3</Superscript>He)nn reaction at a deuteron beam energy of 37 MeV

Inclusive spectra and differential cross sections of the ³H(d, ³He)nn reaction, measured at E _d = 36.9 MeV are presented. The shape of ³He spectra was reconstructed by modeling amplitudes of the neutron-neutron final state interaction (Watson-Migdal amplitudes), sequential decay via the ⁴He* resonance (E* = 21.2 MeV, Γ = 0.7 MeV), and their interferences. The model allowed the determination of the angular dependence of the differential cross section of the ³H(d, ³He)nn reaction accompanied by singlet nn-pair production. The results are compared to the supermultiplet potential model of the lightest nuclei interaction.     

Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of ³H and ⁴He , and for the singlet S -wave ³He -neutron scattering length a ₀(³He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a ₀(³He-n) and the ³H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the ³H binding energy and the ³H charge radius, and the Tjon line. With the ³H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of ³H of (1.6±0.2) fm, for the ⁴He binding energy of (28±2.5) MeV, and for Re{a ₀(³He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between ³H and ³He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the ⁴He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.     

Phase-equivalent transformation which does not affect bound state properties and its manifestation in many-body systems

We propose a phase-equivalent transformation of NN interaction of a new type, the DET-PET transformation, which does not affect the wave function of the bound system (deuteron). The DET-PET properties and its manifestation in many-body systems are studied. In particular, we investigate the correlation of the ³H and ⁴He binding energies (the Tjon line) in calculations with NN potentials obtained by means of DET-PET from the JISP16 NN interaction.     

Investigating neutron-neutron and proton-proton correlations in few-nucleon systems in reactions with two nucleons in the final state

The great disagreement between theory and experiment observed in nd and pd interactions indicates that investigations of mechanisms for various processes in few-nucleon systems should be continued. It is planned to investigate the reactions d + ³H → ³He + (nn) and ³He + d → ³H + (pp) in order to study nn and pp correlations in ³He and ³H nuclei. Test measurements of the d + ²H → ²He + (nn) reaction, performed with the deuteron beam at the Institute of Nuclear Physics, confirm that it is methodologically possible to perform the planned experiments.     

Selected Topics in Correlated Hyperspherical Harmonics

Correlated hyperspherical-harmonic basis functions are used to expand the three- and four-nucleon wave functions. Bound and scattering states are considered. Results for the binding energies of ³H, ³He, and ⁴He calculated using modern two- and three-nucleon forces are given and discussed. For scattering states, results for N-d differential cross section and vector analyzing powers are shown. The importance of the Coulomb and magnetic moment effects are discussed.     

Analyzing Power in Elastic Scattering of Polarized Protons from Neutron-rich Helium Isotopes

The vector analyzing power has been measured for the elastic scattering of neutron-rich ⁶He from polarized protons at 71 MeV/nucleon. Two approaches based on local one-body potentials were applied to investigate the spin-orbit interaction between a proton and a ⁶He nucleus. An optical model analysis revealed that the spin-orbit potential for ⁶He is characterized by a shallow and long-ranged shape compared with the global systematics of stable nuclei. A semi-microscopic analysis with a α + n + n cluster folding model suggests that the inclusion of realistic interaction between a proton and the α core is important in describing the p-⁶He elastic scattering.     

Effect of cluster polarization on the spectrum of the <Superscript>7</Superscript>Li nucleus and on the reaction <Superscript>6</Superscript>Li(<Emphasis Type="Italic">n</Emphasis>, <Superscript>3</Superscript>H)<Superscript>4</Superscript>He

The effect of polarization of the ⁶Li and ³H clusters on the parameters of states of the ⁷Li nucleus and on the cross section for the reaction ⁶Li(n,³H)⁴He was studied. The ⁴He + d + n three-cluster configuration was invoked for this purpose, and cluster dynamics was determined within a microscopic model where the relative motion of the clusters was described in terms of Faddeev amplitudes. The ⁴He + d + n three-cluster configuration made it possible to consider the ⁴He + ³H and ⁶Li + n binary channels, which are dominant in ⁷Li, and to take simultaneously into account the cluster polarization of ⁶Li as a two-cluster subsystemin the ⁴He + d representation and the cluster polarization of ³Has a two-cluster subsystem in the d + n representation.     

Optical reaction cross-sections for light projectiles

The optical reaction cross-sections forn, p,²H,³He,³He and⁴He for several global optical potentials available in the literature have been parametrized in terms of simple empirical expressions which are smooth functions of the target mass number and the projectile energy. The empirical forms are 5–10% accurate over the periodic table and energy-range upto 50 MeV. They can be conveniently used in calculations where the optical reaction cross-sections are required as input. The calculation of proton spectra in the (n, p) reaction at 14 MeV is discussed.     

Simulation of the fben d transitions of lanthanide ions in YPO4 using quantum-chemical calculations

We constructed an effective one-electron Hamiltonian by using the 4f/5d energies and eigenvectors obtained from the first-principles calculation with the relativistic self-consistent discrete variational Slater software package (DV-Xα). From the effective Hamiltonian, we obtained the crystal-field and spin-orbit interaction parameters for the 4f and 5d electrons of lanthanide ions (Ce³⁺, Pr³⁺, Nd³⁺ and Eu³⁺⁾ doped in YPO₄, and these parameters were used to calculate the 4f^N-4f^N-15d transition. Comparison with experiments shows that the obtained parameters are reasonable and the excitation spectra can be well predicted.     

Critical Stability in Nuclei – An Old Problem Revisited

In this paper we will focus on the nucleon-nucleon interaction in relative S-states. The ¹S₀ interaction is known to be close to that for critical two-body binding. We will discuss two approaches to the NN interaction, which are equivalent on-shell but not off-shell. There is a well-defined transformation between these approaches [1]. One (my preferred approach) is to minimize the tensor forces far off-shell, which leads to more rapid convergence, but at the price of significant non-locality. This approach is used in a model of relativistic tensor quenching of OPEP [2]. With non-local NN interactions it is possible to fit not only NN observables, but also the NNN ground-state energies [3]. The other approach is to maximize the role of the and keep the interaction as local as possible [4]. This approach is also internally consistent, but requires additional NNN interactions to fit nuclear data. Also, we discuss briefly a so-called low momentum interaction [5, 6], which fits S-wave phase shifts quite well. This interaction is strongly non-local, and it can be approximated by a schematic separable interaction. Finally, we mention the Nambu–Jona-Lasinio model [7] and a good approximation, the Hulthen potential, which provides some insight into the near critical two-body binding.     

Local three-nucleon interaction from chiral effective field theory

The three-nucleon (NNN) interaction derived within the chiral effective field theory at the next-to-next-to-leading order (N²LO) is regulated with a function depending on the magnitude of the momentum transfer. The regulated NNN interaction is then local in the coordinate space, which is advantageous for some many-body techniques. Matrix elements of the local chiral NNN interaction are evaluated in a three-nucleon basis. Using the ab initio no-core shell model (NCSM) the NNN matrix elements are employed in ³H and ⁴He bound-state calculations. Correspondence: P. Navrátil, Lawrence Livermore National Laboratory, L-414, P.O. Box 808, Livermore, CA 94551, USA     

DWBA analysis of (3He,d) reactions at 90MeV and contributions from the nuclear interior

Differential cross sections of ³He elastic scatterings and (³He, d) reactions have been measured at 90 MeV for ²⁸Si, ⁵⁴Fe, ⁵⁸Ni, ⁹⁰Zr and ¹²⁴Sn. From the optical-model analysis of the elastic scattering, both shallow ($\text{V ? 105}\text{MeV}$) and deep ($\text{V ? 150}\text{MeV}$) potentials of ³He were obtained. The shallow potentials correspond to the ones which were determined uniquely from other measurements extended to more backward angles. The (³He, d) reactions have been analyzed with the DWBA using the shallow and deep potentials for ³He. The calculations using the deep potentials reproduced the data well, but those using the shallow ones did not. The contributions from the nuclear interior were investigated through the radial cutoff in the DWBA. The calculations using the shallow potentials reproduced the data well when the radial cutoffs were introduced. The effects of the radial cutoff were very small when the deep potentials were used. It was found that a much greater reduction of the contributions from the nuclear interior was needed when the shallow potentials were used in the DWBA calculations.     

Analysis of <Superscript>4</Superscript>He+<Superscript>40</Superscript>Ca and <Superscript>4</Superscript>He+<Superscript>44</Superscript>Ti scattering using different optical model potentials

Elastic scattering of ⁴He+⁴⁰Ca and ⁴He+⁴⁴Ti reactions at backward angles has been analyzed using two differentmodels, microscopic and semimicroscopic folding potentials. The derived real potentials supplemented with phenomenological Woods–Saxon imaginary potentials, provide good agreement with the experimental data at energy E_c.m. = 21.8 MeV without need to renormalize the potentials. Coupledchannels calculations are used to extract the inelastic scattering cross section to the low-lying state 2+ (1.083 MeV) of ⁴⁴Ti. The deformation length is obtained and compared with the electromagnetic measurement values as well as those obtained from previous studies.     

Functional relationships of multiparticle distribution functions obtained from the virial theorem

The He(I) photoelectron spectrum of the N₃(X ²H) radical, produced by the rapid gas phase reaction of fluorine atoms with hydrazoic acid, has been recorded. Three bands were observed corresponding to ionization of N₃(X 2H) to the N₃ ⁺ X ³Σ^?, ¹Δ and ¹Σ⁺ states. The vertical ionization energies to the observed ionic states were compared with those obtained from ΔSCF ab initio calculations. Evidence is presented to show that the major pathway of the F+HN₃ reaction occurs via a long-lived intermediate and involves abstraction of a hydrogen atom yielding vibrationally excited HF and the N₃ radical. Consideration of both the photoelectron data and a recent chemiluminescence study of the reaction has led to some re-interpretation of the latter results.     

Parity non-conservation in low energy scattering of nucleons by light nuclei: (II). Results

The analysis developed in the preceding paper is applied to the low energy scattering of longitudinally polarized nucleons by ²H, ³He and ⁴He and of deuterons by ¹H. The sensitivity of the parity non-conserving asymmetry of the total cross section to the weak interaction is probed. The asymmetry is computed for various parity non-conserving nucleon-nucleon potentials in a distorted wave approximation. The asymmetries generally are found to depend sensitively on the parameters of the potential, but are smaller than those predicted for nucleon-nucleon scattering at the same energy.