Independent Particle Shell Model Research Articles

Theoretical description of semi-inclusive T2K, MINERνA and MicroBooNE neutrino-nucleus data in the relativistic plane wave impulse approximation

We present the results of semi-inclusive neutrino-nucleus cross sections within the plane wave impulse approximation (PWIA) for three nuclear models: relativistic Fermi gas, independent-particle shell model, and natural orbital shell model in comparison with the available $\mathrm{CC}0\ensuremath{\pi}$ measurements from the T2K, $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$, and MicroBooNE collaborations where a muon and at least one proton are detected in the final state. Results are presented as a function of the momenta and angles of the final particles, as well as in terms of the imbalances between proton and muon kinematics. The present semi-inclusive formalism is based on fully relativistic microscopic calculations and numerical integrations to produce both lepton and hadron kinematics without relying on further approximations. The analysis reveals that contributions beyond PWIA are crucial to explain the experimental measurements and that the study of correlations between final-state proton and muon kinematics can provide valuable information on relevant nuclear effects such as the Fermi motion and final-state interactions.

Semi-inclusive charged-current neutrino-nucleus cross sections in the relativistic plane-wave impulse approximation

Neutrino-nucleus quasielastic scattering is studied in the plane wave impulse approximation for three nuclear models: the relativistic Fermi gas (RFG), the independent-particle shell model (IPSM) and the natural orbitals (NO) model with Lorentzian dependence of the excitation energy. A complete study of the kinematics of the semi-inclusive process and the associated cross sections are presented and discussed for 40 Ar and 12 C. Inclusive cross sections are also obtained by integrating the semi-inclusive expressions over the outgoing hadron. Results are consistent with previous studies restricted to the inclusive channel. In particular, a comparison with the analytical results for the RFG model is performed. Explicit expressions for the hadronic tensor and the 10 semi-inclusive nuclear responses are given. Theoretical predictions are compared with semi-inclusive experimental data from T2K experiment.

Description of the generalized momentum distribution in finite nuclei within t h e independent-particle shell model

A method for calculating the generalized momentum distribution in finite nuclear systems is presented and discussed within the context of the independent particle shell model. Application to the light closed-shell nuclei 16O and 40Ca is included.

Nuclear theory and event generators for charge-changing neutrino reactions

Semi-inclusive $\mathrm{CC}\ensuremath{\nu}$ cross sections based on factorized cross sections are studied for a selection of spectral function models with the objective of facilitating the choice of models for use as input into event generators. The basic formalism for such cross sections is presented along with an introduction to constructing spectral functions for simple models based on the independent-particle shell model, the relativistic Fermi gas model (RFG), and a local density approximation (LDA) based on the RFG. Spectral functions for these models are shown for $^{16}\mathrm{O}$ along with a more sophisticated model which includes nucleon-nucleon interactions [Alvarez-Ruso et al., Prog. Part. Nucl. Phys. 100, 1 (2018)]. Inclusive and semi-inclusive cross sections are calculated for these models. Although the inclusive cross sections are all of similar size and shape, the semi-inclusive cross sections are substantially different depending upon whether the spectral functions contain some features associated with the nuclear shell model or are based on the RFG and LDA models. Calculations of average values and standard deviations of the initial neutrino energy using the semi-inclusive cross section for the various models are presented and indicate that there may be simple kinematical descriptions of the average neutrino energy which is common to all of these models.

Study of Gamow–Teller strength and associated weak-rates on odd-A nuclei in stellar matter

In a recent study by Cole et al. [A. L. Cole et al., Phys. Rev. C 86 (2012) 015809], it was concluded that quasi-particle random phase approximation (QRPA) calculations show larger deviations and overestimate the total experimental Gamow–Teller (GT) strength. It was also concluded that QRPA calculated electron capture rates exhibit larger deviation than those derived from the measured GT strength distributions. The main purpose of this study is to probe the findings of the Cole et al. paper. This study gives useful information on the performance of QRPA-based nuclear models. As per simulation results, the capturing of electrons that occur on medium heavy isotopes have a significant role in decreasing the ratio of electron-to-baryon content of the stellar interior during the late stages of core evolution. We report the calculation of allowed charge-changing transitions strength for odd-[Formula: see text] [Formula: see text]-shell nuclei ([Formula: see text]Sc and [Formula: see text]Mn) by employing the deformed pn-QRPA approach. The computed GT transition strength is compared with previous theoretical calculations and measured data. For stellar applications, the corresponding electron capture rates are computed and compared with rates using previously calculated and measured GT values. Our finding shows that our calculated results are in decent accordance with measured data. At higher stellar temperature, our calculated electron capture rates are larger than those calculated by independent particle model (IPM) and shell model. It was further concluded that at low temperature and high density regions, the positron emission weak-rates from [Formula: see text]Sc and [Formula: see text]Mn may be neglected in simulation codes.

Nonmesonic weak decay of charmed hypernuclei

We present a study of the nonmesonic weak decay (NMWD) of charmed hypernuclei using a relativistic formalism. We work within the framework of the independent particle shell model and employ a (π, K) one-meson-exchange model for the decay dynamics. We implement a fully relativistic treatment of nuclear recoil. Numerical results are obtained for the one-neutron-induced transition NMWD rates of the N. The effect of nuclear recoil is sizable and goes in the direction to decrease the nuclear decay rate. We found that the NMWD decay rate of is of the same order of magnitude as the partial decay rate for the corresponding mesonic decay , suggesting the feasibility of experimental detection of such heavy-flavor nuclear processes.

Effective proton-neutron interaction near the drip line from unbound states in F25,26

Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The $^{26}$F nucleus, composed of a deeply bound $\pi0d\_{5/2}$ proton and an unbound $\nu0d\_{3/2}$ neutron on top of an $^{24}$O core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The $J^{\pi} = 1^{+}\_1, 2^{+}\_1,4^{+}\_1$ bound states have been determined, and only a clear identification of the $J^{\pi} =3^{+}\_1$ is missing.Purpose: We wish to complete the study of the $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet in $^{26}$F, by studying the energy and width of the $J^{\pi} =3^{+}\_1$ unbound state. The method was firstly validated by the study of unbound states in $^{25}$F, for which resonances were already observed in a previous experiment.Method: Radioactive beams of $^{26}$Ne and $^{27}$Ne, produced at about $440A$\,MeV by the FRagment Separator at the GSI facility, were used to populate unbound states in $^{25}$F and $^{26}$F via one-proton knockout reactions on a CH$\_2$ target, located at the object focal point of the R$^3$B/LAND setup. The detection of emitted $\gamma$-rays and neutrons, added to the reconstruction of the momentum vector of the $A-1$ nuclei, allowed the determination of the energy of three unbound states in $^{25}$F and two in $^{26}$F. Results: Based on its width and decay properties, the first unbound state in $^{25}$F is proposed to be a $J^{\pi} = 1/2^-$ arising from a $p\_{1/2}$ proton-hole state. In $^{26}$F, the first resonance at 323(33)~keV is proposed to be the $J^{\pi} =3^{+}\_1$ member of the $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet. Energies of observed states in $^{25,26}$F have been compared to calculations using the independent-particle shell model, a phenomenological shell-model, and the ab initio valence-space in-medium similarity renormalization group method.Conclusions: The deduced effective proton-neutron interaction is weakened by about 30-40\% in comparison to the models, pointing to the need of implementing the role of the continuum in theoretical descriptions, or to a wrong determination of the atomic mass of $^{26}$F.

Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei

Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay (NMWD) of single-Λ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the only noteworthy difference is that the ratio is appreciably higher and closer to the experimental value in the relativistic calculation. The ability of describing existing data, including the most recent ones, on NMWD of Λ-hypernuclei, warrants application of the formalism to evaluate similar decay processes in charmed nuclei.

Nonmesonic weak decay dynamics from proton spectra of Λ-hypernuclei

A novel comparison between the data and the theory is proposed for the nonmesonic (NM) weak decay of hypernuclei. Instead of confronting the primary decay rates, as is usually done, we focus our attention on the effective decay rates that are straightforwardly related with the number of emitted particles. Proton kinetic energy spectra of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], measured by FINUDA, are evaluated theoretically. The independent particle shell model (IPSM) is used as the nuclear structure framework, while the dynamics is described by the one-meson-exchange (OME) potential. Only for the [Formula: see text], [Formula: see text] and [Formula: see text] hypernuclei it is possible to make a comparison with the data, since for the rest there is no published experimental information on number of produced hypernuclei. Considering solely the one-nucleon-induced (1N-NM) decay channel, the theory reproduces correctly the shapes of all three spectra at medium and high energies (Ep ≳ 40 MeV). Yet, it greatly overestimates their magnitudes, as well as the corresponding transition rates when the full OME (π + K + η + ρ + ω + K*) model is used. The agreement is much improved when only the π + K mesons with soft dipole cutoff parameters participate in the decay process. We find that the IPSM is a fair first-order approximation to disentangle the dynamics of the 1N-NM decay, the knowledge of which is indispensable to inquire about the baryon–baryon strangeness–flipping interaction. It is shown that the IPSM provides very useful insights regarding the determination the 2N-NM decay rate. In a new analysis of the FINUDA data, we derive two results for this quantity with one of them close to that obtained previously.

Nonmesonic Weak Decay Spectra of Light Hypernuclei

The nonmesonic weak decay spectra of light hypernuclei have been evaluated in a systematic way. As theoretical framework we adopt the independent particle shell model with three different one-meson-exchange transition potentials. Good agreement with data is obtained for proton and neutron kinetic energy spectra of $^4_\Lambda$He, and $^5_\Lambda$He, when the recoil effect is considered. The coincidence spectra of proton-neutron pairs are also accounted for quite reasonably, but it was not possible to reproduce the data for the neutron-neutron pair spectra. It is suggested that the $\pi+K$ meson-exchange model with soft monopole form factors could be a good starting point for describing the dynamics responsible for the decays of these two hypernuclei. The $^4_\Lambda$H~ spectra are also presented.

Many-body cascade calculation of final state interactions in C nonmesonic weak decay

We study the nonmesonic weak decay (NMWD) ΛN → nN of hypernucleus induced by one nucleon N = n, p. The whole process is described by two coupled models: one for the primary NMWD of Λ hyperon in the nuclear environment, and the other taking into account the final state interactions (FSI) of the two outgoing nucleons within the residual nucleus. The NMWD dynamics is represented by the one-meson-exchange potential with usual parametrization, while the independent-particle shell model is used as the nuclear structure framework. The FSI are accounted for by a time-dependent multicollisional Monte Carlo cascade scheme, implemented within the CRISP code (Collaboration Rio-São Paulo), which describes in a phenomenological way both the nucleon–nucleon scattering inside the nucleus and the escaping of nucleons from the nuclear surface. An evaporation phase is included to cool down the cascade residual nucleus as well. We analyze the single-nucleon kinetic energy spectra, and the two-nucleon coincidence spectra as a function of both: (i) the sum of the kinetic energies and (ii) the opening angle. The theoretical results are compared with recent data from KEK and FINUDA experiments, obtaining fairly good agreement for inclusive and exclusive kinetic energy spectra. Further theoretical improvements are required to explain angular distributions.

Nonmesonic Hyperon Weak Decay Spectra in 12ΛC

We study the nonmesonic weak decay (NMWD) ΛN → nN of the 12ΛC hypernucleus induced by the nucleon N = n,p with transition rate ΓN. The nuclear process is described by the interplay of two models; one describing the NMWD of hyperon Λ in the nuclear environment, and the other taking into account the Final State Interaction (FSI) of the two outgoing nucleons with the residual nucleus. The first one is done in the framework of the Independent-Particle Shell-Model (IPSM), with the decay dynamics represented by the exchange of π+η+K+ρ+ω+ K*mesons with usual parametrization. For the second one is used a time dependent multicollisional intranuclear cascade schema (implemented in the CRISP code - Collaboration Rio-São Paulo). The results obtained for inclusive and exclusive kinetic energy spectra, and the angular correlation are compared with recent data from KEK and FINUDA experiments. The calculated ratio (Γn/Γp)FSI, between the numbers of emitted back-to-back nn and np pairs, is in good agreement with the experimental data.

Role of the isovector nucleon-nucleus interaction potential in nonmesonic hypernuclear decay

We develop a theoretical finite nucleus framework for the evaluation of the coincidence number of pairs ${N}_{\mathit{nN}}$ and the asymmetry parameter ${a}_{\ensuremath{\Lambda}}$ in nonmesonic hypernuclear decay $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{nN}$, and introduce the effect of final-state interactions. The primary nonmesonic weak hyperon-nucleon decay process is described through the independent-particle shell model. We work within the $2p1h$ subspace of final states, assuming a simple approach for finite nuclei based on the eikonal approximation. An optical potential including the nucleon-nucleus isoscalar and isovector interactions is introduced to take into account the minimum nuclear-medium effects. The calculated values for ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ and ${}_{\ensuremath{\Lambda}}^{12}\mathrm{C}$ show that our treatment of final-state interactions, even those considered as restricted to a subspace of states, brings the independent-particle model results closer to the experimental data.

Spectroscopic factors and strength distributions for the deeply bound orbitals inCa40obtained from the(p⃗,2p)reaction at392 MeV

The cross sections and analyzing powers for the $^{40}\mathrm{Ca}$($\mathrm{pP\vec},2p$) reaction were measured. The strength distributions for the deep-hole states were obtained by a multipole decomposition analysis. The centroid energies and widths of the hole-state strengths of the $1p$ and $1{s}_{1/2}$ orbitals in $^{40}\mathrm{Ca}$ were determined. The spectroscopic factors for the deeply bound $1p$ and $1{s}_{1/2}$ orbitals were extracted as $49\ifmmode\pm\else\textpm\fi{}10%$ and $78\ifmmode\pm\else\textpm\fi{}14%$ of the sum-rule limits of the independent-particle shell model, respectively. A strong influence of the nucleon-nucleon correlations on the spectroscopic factors is suggested.

Weak nonmesonic decay spectra of hypernuclei

We compute one- and two-nucleon kinetic-energy spectra and opening-angle distributions for the nonmesonic weak decay of several hypernuclei, and compare our results with some recent data. The decay dynamics is described by transition potentials of the one-meson-exchange type, and the nuclear structure aspects by two versions of the independent-particle shell model (IPSM). In version IPSM-a, the hole states are treated as stationary, while in version IPSM-b the deep-hole ones are considered to be quasi-stationary and are described by Breit-Wigner distributions.

Nonmesonic weak decay spectra of [formula omitted

To comprehend the recent Brookhaven National Laboratory experiment E788 on HeΛ4, we have outlined a simple theoretical framework, based on the independent-particle shell model, for the one-nucleon-induced nonmesonic weak decay spectra. Basically, the shapes of all the spectra are tailored by the kinematics of the corresponding phase space, depending very weakly on the dynamics, which is gauged here by the one-meson-exchange potential. In spite of the straightforwardness of the approach a good agreement with data is achieved. This might be an indication that the final-state-interactions and the two-nucleon induced processes are not very important in the decay of this hypernucleus. We have also found that the π+K exchange potential with soft vertex-form-factor cutoffs (Λπ≈0.7 GeV, ΛK≈0.9 GeV), is able to account simultaneously for the available experimental data related to Γp and Γn for HΛ4, HeΛ4, and HeΛ5.

Intrinsic asymmetry parameter in nonmesonic hypernuclear decay: analytical proof of the independence on hypernucleus within an independent particle shell model

We derive general analytical expressions for the evaluation of the intrinsic asymmetry parameter in nonmesonic hypernuclear weak decay, within an independent particle shell model framework. Present formalism is valid for even-even, even-odd and odd-odd core hypernucleus. A standard strangeness-changing weak transition potential with exchange of the complete meson octet (π, η, K, ρ, ω, K*) is assumed. Very simple analytical formulas are obtained within the s-wave approximation when we restrict to the π and π+K exchange models, providing an useful and manageable tool to understand the origin of the discrepancies between theoretical and experimental results. Numerical values for 4ΛHe, 5ΛHe, 11ΛB, 12ΛC, 16ΛO, 17ΛO and 28ΛSi hypernuclei are exhibited. Present formalism could be used to understand why new contributions to the exchange potential allow to obtain good agreement with data, as indicated in very recent works. The necessity of a consistent inclusion of: i) different modifications of the exchange potential (two-pion exchange, a1 meson, ΔT = 3/2 terms coming from vector mesons, etc); ii) final state interactions on primary nucleons inside the residual nucleus and also correlations between the free emitted ones; and iii) configuration mixing in the final system, is remarked.

Shell model formalism for all hypernuclei types: A guide to solving the nonmesonic weak decay puzzle

We extend to odd-odd core hypernuclei our independent particle shell model (IPSM) formalism developed previously for the evaluation of the ${\ensuremath{\Gamma}}_{\mathrm{NM}},{\ensuremath{\Gamma}}_{n/p}$, and ${a}_{\ensuremath{\Lambda}}$ hypernuclear weak decay observables. The present procedure reproduces the even-odd and even-even core results as particular cases. Adopting the standard strangeness-changing weak $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{NN}$ transition potential with exchange of the complete pseudoscalar and vector meson octets ($\ensuremath{\pi},\ensuremath{\eta},K,\ensuremath{\rho},\ensuremath{\omega},{K}^{*}$) we get simple analytical expressions for all observables. Numerical values for ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He},{}_{\ensuremath{\Lambda}}^{5}\mathrm{He},{}_{ \ensuremath{\Lambda}}^{11}\mathrm{B},{}_{ \ensuremath{\Lambda}}^{12}\mathrm{C},{}_{ \ensuremath{\Lambda}}^{16}\mathrm{O},{}_{ \ensuremath{\Lambda}}^{17}\mathrm{O}$, and ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$ hypernuclei are obtained and compared with available experimental data, putting special attention on the asymmetry parameter. We remark that, in the present form, the IPSM gives roughly the same value of ${a}_{\ensuremath{\Lambda}}$ for all hypernuclei in contradiction with experiments. We stress the necessity of introducing configuration mixing to go beyond the IPSM taking into account, in a more realistic way, nuclear structure effects. Moreover, one could to include more relevant degrees of freedom, even within the IPSM framework, like: (i) modifications of the exchange potential (two-pion, ${a}_{1}$ meson, $\ensuremath{\Delta}T=3/2$ terms of vector mesons, etc.), (ii) final state interactions accounting for the distortion of the plane waves of emitted nucleons, and (iii) two-nucleon induced decay, as possible ways to solve the puzzle.

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{nN}$ of \ensuremath{\Lambda} hypernuclei ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He}$, ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$, ${}_{\ensuremath{\Lambda}}^{12}\mathrm{C}$, ${}_{\ensuremath{\Lambda}}^{16}\mathrm{O}$, and ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$, as a function of the sum of kinetic energies ${E}_{\mathit{nN}}={E}_{n}+{E}_{N}$ for $N=n,p$. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parametrization. Two versions of the independent-particle shell model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are as follows: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account and (b) IPSM-b, where the highly excited hole states are considered to be quasistationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All np and nn spectra exhibit a series of peaks in the energy interval 110 MeV $<{E}_{\mathit{nN}}<170$ MeV, one for each occupied shell-model state. Within the IPSM-a, and because of the recoil effect, each peak covers an energy interval proportional to ${A}^{\ensuremath{-}1}$ , going from $\ensuremath{\cong}4$ MeV for ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$ to $\ensuremath{\cong}40$ MeV for ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He}$. Such a description could be pretty fair for the light ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He}$ and ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to consider as well the spreading in strength of the deep-hole states and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final-state interactions and of the two-nucleon-induced decay mode.

Quark degrees of freedom inside nuclei: Toward explanation of nuclear properties

Starting with a realistic quark model of nucleon structure, in which quarks are strongly correlated with one another within the nucleon, the light nuclei 2H, 3H, 3He, and 4He can be constructed by assuming similar correlations with the quarks in neighboring nucleons. Importance of color loops created owing to the closure of quark ends of adjacent nucleons is emphasized. Applying the model to larger nucleon systems reveals the emergence of symmetries at the nuclear level that are isomorphic with those known from the independent-particle (shell) model.