Shell-model Expectations Research Articles

Core of F25 studied by the F25(−p ) proton-removal reaction

The $^{9}\mathrm{Be}(^{25}\phantom{{}^{B}e}\mathrm{F}(5/{2}^{+}),^{24}\phantom{{}^{B}e}\mathrm{O}$)X proton-removal reaction was studied at the NSCL using the S800 spectrometer. The experimental spectroscopic factor for the ground-state to ground-state transition indicates a substantial depletion of the proton ${d}_{5/2}$ strength compared to shell-model expectations, similar to the findings of an inverse-kinematics $(p,2p)$ measurement performed at RIBF. The $^{25}\phantom{{}^{B}e}\mathrm{F}$ to $^{24}\phantom{{}^{B}e}\mathrm{O}$ ground-states overlap is considerably less than anticipated if the core nucleons behaved as rigid, doubly-magic $^{24}\phantom{{}^{B}e}\mathrm{O}$ within $^{25}\phantom{{}^{B}e}\mathrm{F}$. We interpret the new results within the framework of the Particle-Vibration Coupling (PVC) model, of a ${d}_{5/2}$ proton coupled to a quadrupole phonon of an effective core. This approach provides a good description of the experimental data, requiring an effective $^{24}\phantom{{}^{B}e}\mathrm{O}^{*}$ core with a phonon energy of $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}$= 3.2 MeV and a $B(E2)\ensuremath{\approx}2.7$ W.u. -- softer and more collective than a bare $^{24}\phantom{{}^{B}e}\mathrm{O}$. Both the Nilsson deformed mean field and the PVC models appear to capture the properties of the effective core of $^{25}\phantom{{}^{B}e}\mathrm{F}$, suggesting that the additional proton polarizes $^{24}\phantom{{}^{B}e}\mathrm{O}$ in such a way that it becomes either slightly deformed or a quadrupole vibrator.

Neutron-unbound states in Ne31

Background: The island of inversion near the $N=20$ shell gap is home to nuclei with reordered single-particle energy levels compared with the spherical shell model. Studies of $^{31}\mathrm{Ne}$ have revealed that its ground state has a halo component characterized by a valence neutron orbiting a deformed $^{30}\mathrm{Ne}$ core. This lightly bound nucleus with a separation energy of only ${S}_{n}=170$ keV is expected to have excited states that are neutron unbound.Purpose: The purpose of this experiment was to investigate the low-lying excited states in $^{31}\mathrm{Ne}$ that decay by the emission of a single neutron.Methods: An 89 MeV/nucleon $^{33}\mathrm{Mg}$ beam impinged on a segmented Be reaction target. Neutron-unbound states in $^{31}\mathrm{Ne}$ were populated via a two-proton knockout reaction. The $^{30}\mathrm{Ne}$ fragment and associated neutron from the decay of $^{31}\mathrm{Ne}$ were detected by the MoNA-LISA-Sweeper experimental setup at the National Superconducting Cyclotron Laboratory. Invariant-mass spectroscopy was used to reconstruct the two-body decay energy ($^{30}\mathrm{Ne}+n$).Results: The two-body decay energy spectrum exhibits two features: a low-lying peak at $0.30\ifmmode\pm\else\textpm\fi{}0.17$ MeV and a broad enhancement at $1.50\ifmmode\pm\else\textpm\fi{}0.33$ MeV, each fit with an energy-dependent asymmetric Breit-Wigner lineshape representing a resonance in the continuum. Accompanying shell-model calculations using the FSU interaction within NuShellX, combined with cross-section calculations using the eikonal reaction theory, indicate that these peaks in the decay energy spectrum are caused by multiple resonant states in $^{31}\mathrm{Ne}$.Conclusions: Excited states in $^{31}\mathrm{Ne}$ were observed for the first time. Transitions from calculated shell-model final states in $^{31}\mathrm{Ne}$ to bound states in $^{30}\mathrm{Ne}$ are in good agreement with the measured decay energy spectrum. Cross-section calculations for the two-proton knockout populating $^{31}\mathrm{Ne}$ states as well as spectroscopic factors pertaining to the decay of $^{31}\mathrm{Ne}$ into $^{30}\mathrm{Ne}$ are used to examine the results within the context of the shell-model expectations.

Double-magic nature of 132Sn and 208Pb through lifetime and cross-section measurements.

Single-neutron states in (133)Sn and (209)Pb, which are analogous to single-electron states outside of closed atomic shells in alkali metals, were populated by the ((9)Be, (8)Be) one-neutron transfer reaction in inverse kinematics using particle-γ coincidence spectroscopy. In addition, the s(1/2) single-neutron hole-state candidate in (131)Sn was populated by ((9)Be, (10)Be). Doubly closed-shell (132)Sn (radioactive) and (208)Pb (stable) beams were used at sub-Coulomb barrier energies of 3 MeV per nucleon. Level energies, γ-ray transitions, absolute cross sections, spectroscopic factors, asymptotic normalization coefficients, and excited-state lifetimes are reported and compared with shell-model expectations. The results include a new transition and precise level energy for the 3p(1/2) candidate in (133)Sn, new absolute cross sections for the 1h(9/2) candidate in (133)Sn and 3s(1/2) candidate in (131)Sn, and new lifetimes for excited states in (133)Sn and (209)Pb. This is the first report on excited-state lifetimes of (133)Sn, which allow for a unique test of the nuclear shell model and (132)Sn double-shell closure.

Reduced neutron spectroscopic factors when using potential geometries constrained by Hartree-Fock calculations

We carry out a systematic analysis of angular distribution measurements for selected ground-state to ground-state ($d,p$) and ($p,d$) neutron transfer reactions, including the calcium isotopes. We propose a consistent three-body model reaction methodology in which we constrain the transferred-neutron bound state and nucleon-target optical potential geometries using modern Hartree-Fock calculations. Our deduced neutron spectroscopic factors are found to be suppressed by $~30$% relative to independent-particle shell-model values, from $^{40}\mathrm{Ca}$ through $^{49}\mathrm{Ca}$. The other nuclei studied, ranging from B to Ti, show similar average suppressions with respect to large-basis shell-model expectations. Our results are consistent with deduced spectroscopic strengths for neutrons and protons from intermediate-energy nucleon knockout reactions and for protons from ($e,{e}^{'}p$) reactions on well-bound nuclei.

Neutron pickup strength in 87Sr from the (p

Differential cross section and analyzing power angular distributions have been obtained for the $^{87}(\mathit{p}\ensuremath{\rightarrow}$,d${)}^{86}$Sr reaction in two measurements using different magnetic spectrometers at incident proton energies of 94.2 and 91.8 MeV. Typical energy resolutions of 70 and 40 keV, respectively, were achieved. Optical-model parameters were obtained by fitting the elastic scattering data measured to laboratory angles of 90\ifmmode^\circ\else\textdegree\fi{} for protons at 94.2 MeV and to 120\ifmmode^\circ\else\textdegree\fi{} for deuterons at 88.0 MeV. Standard exact finite range distorted-wave Born approximation calculations using these optical-model parameters failed to describe the experimental data, while the adiabatic approximation improved the description to some extent. Orbital and total angular momenta, l and j, of the picked-up neutron were extracted from the angular distributions of the differential cross section and analyzing power for all the residual states observed. The rms radius of the 1${g}_{9/2}$ neutron orbital, obtained from magnetic electron scattering, was used in the extraction of strength for this orbital, while rms radii from Hartree-Fock calculations were used for the 2${p}_{1/2}$, 2${p}_{3/2}$, 1${f}_{5/2}$, and 1${f}_{7/2}$ orbitals. The observed 1${g}_{9/2}$ strength, spread over 20 states up to 5.4-MeV excitation, indicates a depletion of about 43% compared to simple shell-model expectations. Similarly, the observed 1${f}_{5/2}$ strength, spread over 17 states, indicates a depletion of about 32%. The weighted summed spectroscopic strength for the 1${g}_{9/2}$ orbital, deduced from the present study, is lower than that obtained from magnetic electron scattering.

Nuclear structure of 86,87Rb from 87,88Si(d, 3He) at 28 MeV

Differential cross sections for 87Sr(d, 3He) 86Rb and 88Sr(d, 3He) 87Rb were measured with the Princeton 27.9 MeV deuteron beam and the quadrupole-dipole-dipole-dipole (QDDD) spectrograph. States of 86Rb and 87Rb up to 1.74 MeV and 1.58 MeV, respectively, were studied with a total resolution of 16keV. Zero-range distorted-wave Born approximation (DWBA) calculations were used to determine l transfers and spectroscopic strengths. If the targets are described as a closed shell for 88Sr and as (v g 9 2 ) −1 for 87Sr, only the 88Sr(d, 3He) 87Rb spectroscopic strengths are close to shell model expectations. The observed 87Sr(d, 3He) 86Rb strengths fall 25% below the shell model sum rule. Hence the data suggest that the proton wave functions of 87Sr contain appreciably more configuration mixing than those of 88Sr. Values for the (πf 5 2 , v g 9 2 ) residual interaction matrix elements are proposed, but must remain tentative until the shortfall of f 5 2 strength is understood.

Measurements of Gamow-Teller strength distributions in masses 13 and 15.

The differenctial cross section and the transverse spin-flip probability have been measured for the dominant transitions in $^{13}\mathrm{C}$(p,n${)\mathrm{}}^{13}$N and $^{15}$N(p,n${)\mathrm{}}^{15}$O at ${\mathrm{E}}_{\mathrm{p}}$=160 MeV. The Gamow-Teller transition strengths deduced from the data show that the major ${(1/2)}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${(3/2)}^{\mathrm{\ensuremath{-}}}$ transitions are strongly quenched relative to the ${(1/2)}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${(1/2)}^{\mathrm{\ensuremath{-}}}$ mirror transitions, in strong disagreement with simple shell-model expectations.

Formula omitted] neutron occupancies in the Ca isotopes

Methods of obtaining nucleon occupancies from total energy-weighted sum rules for spectroscopic factors are described and applied to f 7 2 neutron transfer data for Ca isotopes. The f 7 2 neutron occupancies obtained are consistent with shell model expectations and, for 41Ca and 43Ca, with values previously obtained from an analysis using non-energy-weighted sum rules.

Non-energy-weighted sum rule analysis of one nucleon transfer data on 41Ca, 43Ca, 45Se, 49Ti and 51V and the validity of the shell model

Spin-dependent sum rules for spectroscopic factors have been fitted to experimental data for the transfer of f 7 2 nucleons. The fits give the error in absolute normalizations in terms of the percentage error, σ, in relative spectroscopic factors, and evidence is presented that standard distorted wave Born approximation analyses of light-ion induced reactions give σ < 10%. The sum rule analyses then imply f 7 2 occupancies m agreement with simple shell-model expectations to an accuracy of about 10%. The f 7 2 occupancy deduced for 51V is completely inconsistent with the results of a Hartree-Fock-Bogolyubov calculation.

Spectroscopy of 42Ca from 41Ca(d, p)

Energy levels in 42Ca up to 7.8 MeV have been studied in the neutron capture reaction 41Ca(d, p) 42Ca with 12 MeV bombarding energy. Ninety-four excited states have been identified and angular distributions have been measured in the interval from 5° to 110° by means of a broad-range magnetic spectrograph. The angular distributions together with DW calculations have been used to determine I n values and spectroscopic factors. The f 7 2 strength sum agrees with shell-model expectations if the f 7 2 spectroscopic factors are renormalized by 1 0.75 , in line with other f 7 2 . transfer experiments on 40Ca and 41Ca. A similar renormalization of the l n = 1 spectroscopic factors brings this strength sum in accordance with the shell-model calculations. The effective ( f 7 2 2 ) matrix elements for 42Ca are compared with the corresponding matrix elements of 42Sc and 48Sc. The differences between the three sets of matrix elements are of the order of a few hundred keV or less. The monopole centroid energy of the ( f 7 2 ) 2 multiplet is shifted downwards in the mass-42 nuclei compared to 48Sc, possibly indicating the importance of the monopole pairing force near 40Ca.

Study of the (d, α) reaction applied to 50Cr and 52Cr

The reactions 50Cr(d, α) 48V and 52Cr(d, α) 50V have been carried out at an incident deuteron energy of 15 MeV to investigate the structure of the low-lying levels of 48V and 50V in the light of shell model expectations. Excitation energies and angular distributions have been measured for states up to about 1.5 MeV. For all resolved and strongly excited levels angular momentum transfers could be assigned by comparison with DWBA calculations. For 50V spectroscopic factors have been extracted in relative units assuming pure configurations for the transferred pair of nucleons. The results indicate the existence of seniority and configuration mixing in the level structure of the 48V and 50V isotopes. In both reactions some transitions show characteristic deviations from the direct reaction mechanism. These deviations cannot be reproduced by the DWBA calculations.

Study of the (d, p) Reaction on the Even-ABarium Isotopes 130-138

The ($d, p$) reactions on ${\mathrm{Ba}}^{130,132,134,136,138}$ have been investigated with 12.0-MeV deuterons from the Argonne Tandem Van de Graaff accelerator. Proton spectra were recorded in a broad-range magnetic spectrograph. Many new levels were observed. The ground-state $Q$ values (in MeV) for the ($d, p$) reactions (including the odd-$A$ targets) are found to be 5.269 for $A=130, 4.977$ for $A=132, 4.746$ for $A=134, 6.886$ for $A=135, 4.680$ for $A=136, 6.398$ for $A=137, \mathrm{and} 2.493$ for $A=138$. Proton angular distributions were measured for states up to an excitation energy of about 3 MeV. The observed angular momentum transfers were ${l}_{n}=0, 1, 2, 3, \mathrm{and} 5$, which correspond to the population of states of the $3{s}_{\frac{1}{2}}$ and $2{d}_{\frac{3}{2}}$ configurations below the closed neutron shell at $N=82$ and the $2{f}_{\frac{7}{2}}$, $3{p}_{\frac{3}{2}}$, $3{p}_{\frac{1}{2}}$, $1{h}_{\frac{9}{2}}$, and $2{f}_{\frac{5}{2}}$ configurations above it. From the observed $l$ values, it was possible to assign spins in some isotopes from a knowledge of the spin in other isotopes by taking account of systematic shifts in the $Q$ values of levels and also from shell-model expectations. Distorted-wave Born-approximation calculations were used to extract absolute spectroscopic factors. The problems and uncertainties arising in such calculations were studied in some detail. They derive, in part, from the need to use a sharp radial cutoff to fit the experimental angular distributions; calculations with nonlocal potentials and finite-range approximations did not yield satisfactory fits. Another source of uncertainty is the dependence of the spectroscopic factors upon the geometric parameters of the bound-state potential well. The results are interpreted with the help of pairing theory; centers of gravity and single-particle energies are deduced.

Deformed-core model results for nuclear beta-moments

It is found that core-deformations, as treated by Nilsson, can account for a major part of the many types of discrepancy between simple shell-model expectations and observed trends in beta-decays rates, among very light as well as heavier nuclei. Not only are the well-known suppressions of normal allowed transitions relative to shell-model expectations treated, but similar suppressions among forbidden transitions, distinguished here for the first time. Significant confirmation for applications of the deformed-core picture even to mirror nuclei comes from a correlation discovered between certain l-forbidden decay enhancements and super-allowed decay suppressions.