Detailed Shell Model Calculations Research Articles

Neutron knockout ofBe12populating neutron-unbound states inBe11

Neutron-unbound resonant states of 11Be were populated in neutron knock-out reactions from 12Be and identified by 10Be-n coincidence measurements. A resonance in the decay-energy spectrum at 80(2) keV was attributed to a highly excited unbound state in 11Be at 3.949(2) MeV decaying to the 2+ excited state in 10Be. A knockout cross section of 15(3) mb was inferred for this 3.949(2) MeV state suggesting a spectroscopic factor near unity for this 0p3/2- level, consistent with the detailed shell model calculations.

Proton capture reaction rates in the rp process.

Detailed shell-model calculations have been performed to study the structure of excited states in neutron deficient T=1, T=3/2, and T=2 nuclei in the mass range A=23--43. Excitation energies, single-particle spectroscopic factors, as well as \ensuremath{\gamma}-transition strengths were computed. On the basis of these results new reaction rates were calculated for proton capture on the T=1/2 nucleus $^{35}\mathrm{Ar}$, on the odd-odd T=1 nuclei $^{24}\mathrm{Al}$ and $^{32}\mathrm{Cl}$, on the even-even T=1 nuclei $^{26}\mathrm{Si}$, $^{30}\mathrm{S}$, $^{34}\mathrm{Ar}$, and $^{42}\mathrm{Ti}$ and the T=3/2 nuclei $^{23}\mathrm{Al}$, $^{27}\mathrm{P}$, $^{31}\mathrm{Cl}$, and $^{35}\mathrm{K}$. The new reaction rates are compared with the results of statistical model calculations as well as with previous estimates. The consequences of these new rates for the reaction flow and the rp process nucleosynthesis at different stellar temperature and density conditions will be discussed.

Electric and magnetic dipole transitions from broad s-wave neutron resonance in even-even sd-shell nuclei.

Observations have been performed for electromagnetic transitions from the broad {ital s}-wave neutron resonances at 658 keV in {sup 24}Mg, at 180 keV in {sup 28}Si, and at 103 keV in {sup 32}S. Capture gamma rays were measured with an anti-Compton NaI(Tl) detector, using a neutron time-of-flight technique. {ital E}1 and {ital M}1 transitions from those resonances to low-lying states with a strong single-particle character were found. The deduced partial radiative widths for {ital E}1 transition are in excellent agreement with the Lane-Mughabghab valence-capture model calculations taking the neutron effective charge, {minus}{ital Ze}/{ital A}. Moreover, it is shown that essential features of the observed {ital E}1 and {ital M}1 transitions can be well explained by assuming a configuration-mixing wave function, {Psi}{sub {ital i}}(1/2{sup +})={ital a}(0{sup +}{direct product}1/2{sup +})+{ital b}(1{sup +}{direct product}1/2{sup +})+{ital c}(1{sup +}{direct product}3/2{sup +}), for each resonance. The {ital M}1 transition strengths are compared also with more detailed shell model calculations in the model space of full ({ital sd}){sup {ital n}} configurations, using the Wildenthal effective interaction.

M4 excitations in 13C.

Cross sections for the 9.50, 16.08, and 21.47 MeV M4 transitions in $^{13}\mathrm{C}$ have been measured by inelastic electron scattering. Isoscalar and isovector transition amplitudes were deduced by comparison with (\ensuremath{\pi},\ensuremath{\pi}') and (p,p') data. In particular, the transition amplitudes obtained for the 9.50 MeV excitation give a remarkably consistent description of all existing measurements. A comparison was made with M4 transitions in other carbon isotopes, $^{12}\mathrm{C}$ and $^{14}\mathrm{C}$. In each case, detailed shell model calculations accurately predict the energies, relative strengths, and isospin character of the observed M4 transitions. However, the shell model gives (e,e') M4 cross sections that exceed the data by a factor of 2.

An effective Skyrme-type interaction for nuclear structure calculations: (II). Excited-state properties

A universal effective NN interaction SkE of the Skyrme type has been proposed, suitable for both ground and excited states in nuclei throughout the nuclear mass table. In this second part (II) the behaviour of the SkE force as a particle-particle and particle-hole effective interaction is studied. We show the ability of SkE to reproduce all two-particle (two-hole) valence nucleon spectra. A detailed study for 18O and 130Sn is carried out. The definitely determined SkE interaction is also applied as a particle-hole interaction and detailed shell-model calculations for the light 16O and heavy 208Pb nuclei are discussed. We also concentrate on the description of giant multipole resonances throughout the whole nuclear mass region.

Spin flip transitions inC13andF19probed with the (π−, γ) reaction

Photon spectra from radiative capture of stopped negative pions captured by $^{13}\mathrm{C}$ and $^{19}\mathrm{F}$ nuclei have been measured with a high resolution pair spectrometer. In the bound region transitions have been observed to $^{13}\mathrm{B}$(g.s.), $^{13}\mathrm{B}$(3.5 MeV), $^{19}\mathrm{O}$(g.s.), $^{19}\mathrm{O}$(4.9 MeV), and $^{19}\mathrm{O}$(6.3 MeV). In addition, strong transitions to narrow states above the neutron separation threshold were observed in both cases. The results for $^{13}\mathrm{C}$ are in agreement with detailed shell model calculations of this process. Major strength is observed for states formed by coupling extra nucleons or holes to the spin-quadrupole ${d}_{\frac{5}{2}}$ and ${d}_{\frac{3}{2}}$, ${J}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ states in $^{16}\mathrm{O}$. The $^{13}\mathrm{C}({\ensuremath{\pi}}^{\ensuremath{-}}, \ensuremath{\gamma})^{13}\mathrm{B}_{\mathrm{g}.\mathrm{s}.}$ branching ratio is shown to be consistent with beta decay and electroexcitation data, through a combined phenomenological analysis. The observed transition strengths are accounted for by matrix elements of the spin-density operators ${[\ensuremath{\sigma}\ifmmode\times\else\texttimes\fi{}{Y}_{0}]}^{1}{t}^{+}$ and ${[\ensuremath{\sigma}\ifmmode\times\else\texttimes\fi{}{Y}_{1}]}^{2}{t}^{+}$.NUCLEAR REACTIONS $^{13}\mathrm{C}({\ensuremath{\pi}}^{\ensuremath{-}}, \ensuremath{\gamma})$, $^{19}\mathrm{F}({\ensuremath{\pi}}^{\ensuremath{-}}, \ensuremath{\gamma})$; measured normalized $I({E}_{\ensuremath{\gamma}})$; deduced upper limit on $\ensuremath{\delta}(\frac{E2}{M1})$ for $^{13}\mathrm{C}$\ensuremath{\rightarrow}$^{13}\mathrm{B}$(g.s.) at $q=125$ MeV/c, systematics of SIGDR in $12\ensuremath{\le}A\ensuremath{\le}20$. Stopped ${\ensuremath{\pi}}^{\ensuremath{-}}$; pair spectrometer; 850 keV at 129.4 MeV.

Beta decay ofO21

The radioisotope /sup 21/O was produced in the /sup 9/Be(/sup 18/O,2pa)/sup 21/O reaction using 80--110-MeV /sup 18/O ions. Activities emerging from a Be target foil were stopped in a He gas cell and transferred to a counting area where ..gamma.. and ..beta.. rays were measured using Ge(Li) and plastic detectors. Thirteen g rays were observed in singles, g-g, or b-g coincidence measurements following the b decay of /sup 21/O to known excited states of /sup 21/F at 1730, 3460, 3518, (3639), 4572, and 4584 keV. Detailed information on the properties of the /sup 21/F energy levels was obtained. By stopping the gas flow and measuring the decay of g rays, the half-life of /sup 21/O was found to be 3.42 +- 0.10 sec. ..beta.. end-point energies measured by ..beta..-..gamma.. coincidences lead to a mass excess of 8105 +- 175 keV for /sup 21/O in agreement with more accurate reaction Q values. Detailed shell-model calculations were carried out and reproduce the main features of the /sup 21/O decay scheme.

Sp(4, R) symmetry in light nuclei

A classification of nuclear states according to the non-compact Lie algebra Sp(4, R) is investigated. This model strikes a compromise between the Sp(6, R) and Sp(2, R) models and furnishes a practical, yet algebraically simple means for selecting those shell-model core excitations which are needed for the development of quadrupole collectivity in rotational bands of deformed nuclei. Applications to rotational bands in 24Mg and 16O, including shell-model excitations with excitation energies up to 10ħω, show that the core excitations needed to fit observed E2 rates in these nuclei are too large to be treated by perturbation theory. Despite this, a definite symplectic band structure emerges. The nature of the core excitations is very simple, so that it may be feasible to incorporate such symplectic excitation structures into more detailed shell-model calculations.

Alpha and proton decay of the isoscalar E2 resonance in 16O and 40Ca

The large α- over proton-decay ratio of the giant isoscalar quadrupole resonance in 16O at E x≈ 21 MeV ( Γ rms ≈ 6 MeV) after excitation by inelastic α -particle scattering is explained within the framework of SU(3) including predominantly 1p-1h excitations. A detailed shell model calculation gives similar results. It is shown that the E2 resonance in 16O decays preferentially into the 4.43 MeV 2 + state in 12C and an α-particle in an l = 4 partial wave. A similar study in 40Ca reveals that the α- over proton-decay ratio is considerably reduced compared to the ratio for 16O reproducing the experimental trend.

Study of the level structure of 62Ni

The properties of excited states in 28 62Ni 34 populated by means of the 59Co(α, pγ) 62Ni reaction were investigated. The Doppler-shift attenuation method was employed to determine the mean lives of 20 levels up to an excitation energy of 4151 keV. A comprehensive level and decay scheme is proposed. Detailed shell-model calculations have been made of the M1 and E2 transition matrix elements for depopulation of states which, when compared with experiment, do not support an interpretation based on an inert 28 56Ni 28 core. This is strongly confirmed by use of this model spectroscopy in the analyses of inelastic proton scattering data to the 2 1 + and 3 1 − states in 62Ni.

Level structure and lifetimes of excited states in 48Ti

The properties of excited states in 22 48Ti 26 populated by means of the 45Sc(α, pγ) 48Ti reaction were investigated. The Doppler-shift attenuation method was employed to determine the mean lives of 16 levels up to an excitation energy of 4073 keV. Proton-γ coincidence techniques were used to record simultaneously the Doppler-shifted de-excitation γ-rays emitted at 26 and 154 degrees to the incident beam direction. A comprehensive level and decay scheme is proposed. Detailed shell-model calculations have been made of M1 and E2 transition matrix elements for depopulation of states whose lifetimes have been measured. Salient nuclear structure aspects of this “self-cross-conjugate” nucleus are examined in light of critical comparisons of measured and calculated Ml and E2 reduced transition probabilities.

Mean lifetimes of levels in 55Co

The mean lifetimes of levels in 55Co below 5.2 MeV have been investigated with the Doppler-shift attenuation method and the 54Fe( 3He, d) 55Co reaction at 12 MeV. Scattered particles were detected in two E- ΔE telescopes at ±55° with respect to the beam axis, in coincidence with γ-rays observed at 90° and 130° in a 50 cm 3 Ge(Li) detector. Mean lifetimes are reported for the following levels (energy in keV, lifetime in fs): 2166 (139±18), 2566 (680±200), 2923 (>245), 2939 (190±65), 3303 (99±22), 3323 (54±15), 3642 (680 −300 +400), 3943 (>170), 4164 (54±15), 4180 (<16), 4722 (<33), 4749 (<70) and 5174 (<40). The experimental results are compared with a detailed shell-model calculation.

Photoproduction ofπ+fromV51

The reaction $^{51}\mathrm{V}(\ensuremath{\gamma}, {\ensuremath{\pi}}^{+})^{51}\mathrm{Ti}$ is investigated within the impulse approximation. A detailed shell-model calculation is carried out to determine the character of the final nuclear states. We discuss the dependence of the reaction on the single-nucleon production amplitudes, nuclear wave functions, and simulated final state interactions.NUCLEAR REACTIONS $^{51}\mathrm{V}(\ensuremath{\gamma}, {\ensuremath{\pi}}^{+})$ calculated total $\ensuremath{\sigma}$.

The (t, p) reaction to the low-lying levels of the zirconium isotopes

The (t, p) reaction on the isotopes 90,92,94,96Zr has been carried out at a bombarding energy of 20 MeV. Only weakly excited O + states are observed in 92Zr and 94Zr while the first excited O + state in 96Zr is strongly excited. No O + states are seen in 98Zr. The results indicate a trend for ground state excitations intermediate between simple shell model and pairing vibration theory. The low-lying levels of 92Zr and 94Zr are described by detailed shell model calculations. There is no indication in these nuclei of the rapid onset of deformation previously reported in 100Zr, nor is there any evidence for an excited rotational band structure in any of the zirconium nuclei studied.

New Aluminum Isotope; Mass andβDecay of theTz=52NuclideAl31and the Mass ofP34

The first reported measurements of the $\ensuremath{\beta}$ decay, half-life, and mass of $^{31}\mathrm{Al}$ are presented. The new activity was produced by the $^{18}\mathrm{O}(^{18}\mathrm{O}, \ensuremath{\alpha}p)^{31}\mathrm{Al}$ reaction using 41-MeV incident $^{18}\mathrm{O}$ ions, and was transferred pneumatically to a remotely located station where delayed $\ensuremath{\gamma}$ rays and $\ensuremath{\beta}$ rays were counted with Ge(Li) and NE 102 detectors, respectively. $\ensuremath{\gamma}$-ray energies (in keV) and relative intensities for the $^{31}\mathrm{Si}$ daughter transitions are 621.81\ifmmode\pm\else\textpm\fi{}0.30 (9.94\ifmmode\pm\else\textpm\fi{}0.65), 752.23 \ifmmode\pm\else\textpm\fi{}0.30 (18.5\ifmmode\pm\else\textpm\fi{}0.8), 1564.49\ifmmode\pm\else\textpm\fi{}0.30 (17.3\ifmmode\pm\else\textpm\fi{}1.6), 1694.73\ifmmode\pm\else\textpm\fi{}0.30 (58.9\ifmmode\pm\else\textpm\fi{}1.6), and 2316.64\ifmmode\pm\else\textpm\fi{}0.40 (72.8\ifmmode\pm\else\textpm\fi{}1.8). The $^{31}\mathrm{Si}$ excitation energies (in keV) and relative $\ensuremath{\beta}$ branching intensities are 752.24\ifmmode\pm\else\textpm\fi{}0.30 (3.0), 1694.78\ifmmode\pm\else\textpm\fi{}0.30 (49.0\ifmmode\pm\else\textpm\fi{}1.7), and 2316.73\ifmmode\pm\else\textpm\fi{}0.40 (100\ifmmode\pm\else\textpm\fi{}2.5). A tentative $\ensuremath{\beta}$- ray transition to a state at ${E}_{x}=2787.7\ifmmode\pm\else\textpm\fi{}0.8$ keV is also observed. Upper limits on the strength of some possible $\ensuremath{\gamma}$-ray transitions following $\ensuremath{\beta}$ decay to higher levels are given. $^{31}\mathrm{Al}$ decays with a half-life of 644\ifmmode\pm\else\textpm\fi{}25 msec. By measuring the energy spectra of $\ensuremath{\beta}$ rays populating the second and third excited states of $^{31}\mathrm{Si}$ the mass excess of $^{31}\mathrm{Al}$ has been measured to be -15008\ifmmode\pm\else\textpm\fi{}100 keV. The mass excess of $^{34}\mathrm{P}$ has been remeasured by a similar technique to be -24 550\ifmmode\pm\else\textpm\fi{}90 keV, and this value has been used to revise previous predictions for the masses of $^{33}\mathrm{Si}$ and $^{35}\mathrm{P}$. The masses of several ${T}_{z}=\frac{5}{2}$ and ${T}_{z}=3$ nuclides in the $2s\ensuremath{-}1d$ shell are compared with theoretical estimates. The $\ensuremath{\beta}$-decay measurements for $^{31}\mathrm{Al}$ are shown to be in poor agreement with simple collective-model calculations, and in good agreement with recent detailed shell-model calculations.

Gamma-Ray Decay of the Low-Lying Levels ofCl34

The excitation energies and $\ensuremath{\gamma}$-ray decay modes of the low-lying states of ${\mathrm{Cl}}^{34}$ have been studied using the ${\mathrm{S}}^{32}({\mathrm{He}}^{3},p\ensuremath{\gamma}){\mathrm{Cl}}^{34}$ reaction. Some lifetime limits were obtained by the Dopplershift-attenuation method. The lifetimes of the $({J}^{\ensuremath{\pi}},T)=({1}^{+},0)$ levels at 461 and 666 keV, and the (${2}^{+}$, 0) level at 1230 keV were measured to be 7.1 \ifmmode\pm\else\textpm\fi{} 0.7, 12.8 \ifmmode\pm\else\textpm\fi{} 1.0, and 19.4 \ifmmode\pm\else\textpm\fi{} 1.4 psec, respectively, using the recoil-distance (plunger) technique with the ${\mathrm{P}}^{31}(\ensuremath{\alpha},n\ensuremath{\gamma}){\mathrm{Cl}}^{34}$ reaction. The transition strengths from these three levels are discussed qualitatively in terms of calculations involving simple configurations, and are compared with recent detailed shell-model calculations.

In-beam gamma-ray spectroscopy of even Mo and Ru isotopes

Excited states of 92, 94, 96, 98Mo and 94, 96, 98, 100,102Ru were studied by in-beam γ-ray spectroscopy. The decays of levels populated by the (α, 2n) reaction on even isotopes of Zr and Mo were studied by measurement of the γ-singles spectrum, beam-γ-delay, γγ- coincidences (prompt and delayed), and γ-ray angular distributions. The most notable new feature of these experiments is the use, in-beam, of a sensitive coincidence technique, employing two Ge(Li) spectrometers in conjunction with a two-parameter incremental data-acquisition system, to establish the placement of weak transitions. The level schemes are compared with previous studies of these nuclei. A considerable number of new levels, predominantly of high spin (I > 6), were observed. The observed levels are analyzed in terms of systematics and, where available, detailed shell-model calculations. A general description in terms of excitations in the low-lying orbitals outside a 38-proton+50-neutron core appears adequate to explain much of the data, particularly in those nuclei near the 50-neutron shell. The data are also compared to recent macroscopic calculations of quasi-rotational bands, the VMI model. The observed spin distribution in the residual nuclei indicates a net loss of angular momentum in the emission of neutrons and/or unresolved γ-rays. Calculations based on a microscopic model for neutron evaporation suggest that, with a moment-of-inertia parameter ∮ = 0.5 ∮ rigid, the angular-momentum loss can be accounted for entirely by the neutrons, whereas for ∮ > 0.5 /t0 rigid, some of it must reside in the unplaced γ-ray transitions.

Nuclear-Structure Calculations forCu59and Odd Nickel Isotopes

A detailed shell-model calculation is carried out to discuss the properties of the low-lying states of ${\mathrm{Cu}}^{59}$ and ${\mathrm{Ni}}^{59}$ nuclei. An inert ${\mathrm{Ni}}^{56}$ core is assumed and the three extracore particles are considered to occupy the $1{p}_{\frac{3}{2}}$, $0{f}_{\frac{5}{2}}$, and $1{p}_{\frac{1}{2}}$ orbitals. The effect of including the $0{g}_{\frac{9}{2}}$ orbital is studied. The renormalized reaction matrix elements as derived by Kuo and Brown for this mass region are used. A comparison between the observed and calculated energy levels is made and the wave functions obtained are used to calculate the spectroscopic factors for the ${\mathrm{Ni}}^{58}({\mathrm{He}}^{3},d){\mathrm{Cu}}^{59}$ and ${\mathrm{Ni}}^{58}(d,p){\mathrm{Ni}}^{59}$ reactions. The odd-mass Ni isotopes (${\mathrm{Ni}}^{59}$, ${\mathrm{Ni}}^{61}$, ${\mathrm{Ni}}^{63}$, ${\mathrm{Ni}}^{65}$) are then described by the modified Tamm-Dancoff approximation (MTDA) method. The MTDA results for odd Ni isotopes are found to be in quite satisfactory agreement with experiment. These results together with the previous results for even Ni isotopes by Roy, Raj, and Rustgi lead us to believe that the Kuo-Brown matrix elements in conjunction with the MTDA method give a good description of all the Ni isotopes.

The giant dipole excitations of 12C in the open shell tamm-dancoff approximation and in the intermediate-coupling shell model

Particle-hole and detailed shell model calculations have been performed for the giant dipole excitations of 12C. It is found that the particle-hole approximation gives the correct gross structure of the photo-resonance provided the particle-hole excitations are referred to the intermediate coupling ground state rather than to the unrealistic closed 1p 3 2 -shell.

Experimental High-Resolution Investigation and Shell-Model Interpretation of theCa49Ground-State Analog

Excitation functions for $^{48}\mathrm{Ca}(p,p)$ at 165\ifmmode^\circ\else\textdegree\fi{} and 105\ifmmode^\circ\else\textdegree\fi{} have been measured from 1.93 to 2.01 MeV.Inaddition, the reactions $^{48}\mathrm{Ca}(p,n)^{48}\mathrm{Sc}$ and $^{48}\mathrm{Ca}(p,n\ensuremath{\gamma})^{48}\mathrm{Sc}$ have been observed. Spins, parities, total and partial widths have been assigned. Eleven resonances are observed, eight of which have ${J}^{\ensuremath{\pi}}={\frac{3}{2}}^{\ensuremath{-}}$ and are associated with the $^{49}\mathrm{Ca}$ ground-state analog. These ${\frac{3}{2}}^{\ensuremath{-}}$ levels are interpreted in terms of a detailed shell-model calculation. The importance of $4p\ensuremath{-}3h$ and higher configurations is noted.