Shell-model calculations inA=28–32 nuclei

Shell-model calculations for positive-parity levels of A=28–32 nuclei have been performed in a 1d_5/2 2s_1/2 1d_3/2 configuration space. Configuration mixing of at most 250 lowest-lying pure configurations for each (A, J, T) set was taken into account. By a variation of the four effective interaction (MSDI) parameters and three single-particle energies a search was made for the best fit of the calculated energies to the experimental values. The average deviation between theory and experiment for the energies of the 110 fitted levels is 0.44 MeV. By adjusting all the 63 two-body matrix elements (ASDI) and the three single-particle energies, the average deviation of the binding energies was reduced to 0.16 MeV. For the lowest 10–15 levels in all A=28–32 nuclei a one to one correspondence exists between theory and experiment. Electromagnetic transition strengths were calculated both with MSDI and with ASDI wave functions. The ASDI wave functions reproduce the experimental E2 data much better than the MSDI wave functions. For the M1 transition strengths only a minor improvement has been achieved.     

Shell-model calculations with an adjusted surface-delta interaction (I) application to spectroscopic factors inA=24–28 nuclei

Shell-model calculations have been performed for positive-parity levels of theA=24–28,T≦3/2 nuclei in a 1d _5/22s _1/21d _3/2 configuration space. The space, for each (A, J, T) set, was restricted such that only mixing of less than about 300 low-lying pure configurations was allowed. An effective interaction (MSDI) was used of which the parameters have been determined by a fit of the calculated energies to the experimental values. This resulted in an averaged deviation of 0.52 MeV for 67 fitted levels. Spectroscopic factors have been calculated with the derived wave functions. In order to obtain better agreement for the energies, all of the 63 two-body matrix elements and three single-particle energies were adjusted systematically. The wave functions derived from this adjusted set of matrix elements denoted by ASDI yield considerably better spectroscopic factors. For comparison, the spectroscopic factors have also been calculated in a 1d _5/22s _1/2 model space. The omission of the 1d _3/2 subshell was found to result in a substantially poorer agreement for the spectroscopic factors for 1d _5/2 and 2s _1/2 transfer.     

Shell-model calculations for the zinc isotopes

Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 0}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits outside a closed “⁵⁶Ni” core. The effective Hamiltonian used was one obtained by Koops and Glaudemans from a fit to Ni and Cu level energies. An average absolute deviation of 0.19 MeV between the calculated and experimental ground-state binding energies is obtained for the A = 62?68 Zn isotopes. Good agreement is also found between most calculated and experimental excitation energies and spectroscopic factors for single-nucleon transfer for the low-lying levels in these nuclei. Experimentally known B(E2) values are generally well reproduced by the present model with effective charges of 1.0 ± 0.1 and 1.6 ± 0.2 for the neutron and proton, respectively. Magnetic dipole as well as Gamow-Teller transitions are not well accounted for by these calculations and seem to be sensitive to excitations of the ⁵⁶Ni core.     

A high resolution study of 26Al via the (p,d) reaction

Excitation energies and angular distributions of ²⁶Al levels in the first 6 MeV of excitation have been measured with the ²⁷Al(p, d)²⁶Al reaction at E_p = 35 MeV. Deuteron spectra were analyzed with an Enge split-pole magnetic spectrograph and recorded on nuclear emulsions (experimental resolution ≈ 6 keV, FWHM); supplementary data were recorded with position-sensitive wire proportional counters. The angular distributions were analyzed with the DWBA to extract the l-values and associated spectroscopic factors of the neutron transfers. The results for excitation energies, l-values, spectroscopic factors, and values of J^π, T are discussed in terms of previous experimental and theoretical work and in the light of new shell-model calculations for this system.     

Spectroscopic information from the63Cu(p, γ)64Zn reaction in the GDR region

The proton capture cross sections for the reaction⁶³Cu(p, γ_i)⁶⁴Zn leading to several resolved states in the⁶⁴Zn nucleus have been measured forE _p =6.5–11.0 MeV. The excitation functions have been reproduced by the combined CN and DSD models. The extracted spectroscopic factors compared with those derived from the stripping reaction are found to show a distinct correlation.     

The gamma decay of analogue states in61Cu

Resonances in the reaction⁶⁰Ni(p, γ)⁶¹Cu have been studied in the proton energy rangesE _p=1840–1880 keV and 2220–2300 keV. Decay schemes and branching ratios have been determined for a number of resonances, three of which are identified as analogue fragments of the 283 keV (1/2^?) and 656 keV (3/2^?) states in⁶¹Ni. The split analogue components of the 283 keV state atE _x≈6.6 MeV are seen to decay significantly to a group of states in the region of excitation 3–4 MeV. Gamma ray angular distributions yield the following resonance spins:E _p=2248 keV,J=3/2;E _p=2263 keV,J=5/2. Also, the⁶¹Cu ground stateβ ⁺ decay to parent levels in⁶¹Ni has been compared to the respective analogue stateM1 gamma decay to the⁶¹Cu ground state.     

Role of cross-shell excitations in the reaction 54Fe($$ \vec d $$, p)55Fe

The reaction ⁵⁴Fe(, p)⁵⁵Fe was studied at the Munich Q3D spectrograph with a 14MeV polarized deuteron beam. Excitation energies, angular distributions and analyzing powers were measured for 39 states up to 4.5MeV excitation energy. Spin and parity assignments were made and spectroscopic factors deduced by comparison to DWBA calculations. The results were compared to predictions by large-scale shell model calculations in the full pf -shell and it was found that reasonable agreement for energies and spectroscopic factors below 2.5MeV could only be obtained if up to 6 particles were allowed to be excited from the f _7/2 orbital into p _3/2 , f _5/2 , and p _1/2 orbitals across the N = 28 gap. For levels above 2.5MeV the experimental strength distribution was found to be significantly more fragmented than predicted by the shell model calculations.     

Evidence of non-statistical structures in the elastic and inelastic scattering of58Ni+58Ni and58Ni+62Ni and intermediate dinuclear states

Excitation functions and angular distributions of⁵⁸Ni+⁵⁸Ni and⁵⁸Ni+⁶²Ni scattering at energies just above the Coulomb barrier have been measured aroundθ _cm=90° in energy stepsΔE _cm=0.25 MeV fromE _cm ? 110 MeV toE _cm ? 120 MeV for⁵⁸Ni+⁵⁸Ni and fromE _cm ? 110 MeV toE _cm ? 118 MeV for⁵⁸Ni+⁶²Ni. Evidence for structure of non-statistical character has been found in the angle-summed excitation functions; this evidence is corroborated by the analysis of the angular distributions. This is the first time that non-statistical structure in elastic and inelastic scattering is reported with high confidence level for this mass and excitation energy ranges. Attempts are presented to understand the nature of this structure, including the presence of intermediate dinuclear states and virtual states in a potential well.     

The (d, 6Li) reaction on 12C, 16O, 24Mg, 40Ca and 58Ni at 54.25 MeV

The (d, ⁶Li) reaction was studied at E_d = 54.25 MeV on the target nuclei ¹²C, ¹⁶O, ²⁴Mg, ⁴⁰Ca and ⁵⁸Ni. The data were analyzed with finite-range DWBA calculations. The absolute values of the α-cluster spectroscopic factors and the target mass dependence of the relative S_α were in agreement with those in the (p, pα) reaction at E_p = 100 and 157 MeV. The theoretical calculations of the relative S_α were in better agreement with the experimental data at higher energy than at the lower energies.     

Groundstate proton radioactivity of nuclei in the tin region

Proton radioactivities with decay energies of (0.98±0.08) MeV and (0.83±0.08) MeV were produced by the fusion reactions⁵⁸Ni+⁵⁸Ni→¹¹⁶Ba ? and⁵⁸Ni+⁵⁴Fe→¹¹²Xe ?, and their halflives were measured to be (33±7) μs and (109±17) μs, respectively. The intensities of the lines correspond to production cross sections of about 30 μb and 40 μb. The two activities are assigned to the direct proton decay of¹¹³Cs and¹⁰⁹I. The measured halflives are compared with values calculated ford _5/2 andg _7/2 groundstates of¹⁰⁹I and¹¹³Cs and spectroscopic factors are deduced for the decays. An extensive search for the proton decay of¹⁰⁵Sb, produced in the reaction⁵⁰Cr(⁵⁸Ni,p2 n)¹⁰⁵Sb, had a negative result, excluding decay energies between 0.5 MeV and 1.5 MeV for halflives between 10 ns and 5 s.     

Investigation of65Cu by means of the average resonance proton capture method

The⁶⁴Ni(p, γ)⁶⁵Cu reaction has been studied in the proton energy rangeE _p =2.05–2.55 MeV. The gamma-ray spectra were recorded with a three-crystal pair spectrometer at proton energy differences of 19 keV covering the proton energy range. An average gamma-ray spectrum was formed by adding all the individual spectra after proper adjustment as a result of the alterations in proton energy. The intensities of the gamma rays to final states with knownJ ^π-values were tested against theoretical calculations based on the Hauser-Feshbach theory. The gamma-ray strength function for energies lower than 9 MeV has been extracted from the experiment.     

Non-normal parity states in mass 10–15 nuclei

The modified surface delta interaction (MSDI) is used as the effective two-nucleon residual interaction in extensive shell-model calculations forA=10–15 nuclei; a He-4 core andj-j coupled extra-core nucleon configurations of the formP _3/2 ⁿ P _1/2 ^m (1d _5/2,2s _1/2)¹ are employed. Level energies and wave functions for low-lying non-normal parity states are first obtained from a simultaneous fit to experimental energies over the entire 10–15 mass range. The wave functions are next tested by comparing predicted nuclear properties with experimental data: single-nucleon spectroscopic factors, beta decay lifetimes,M1 andE2 radiative transition widths as well asE1 andM2 radiative widths are calculated. In general good agreement between experiment and theory is obtained.     

Core polarization and 5/2+ states in91Nb

The energies and spectroscopic factors ofJ ^π=5/2⁺ states of nucleus⁹¹Nb excited via a reaction transferring a proton to the 2d _5/2 orbit of⁹⁰Zr target state have been calculated. Effective two-body interaction used has been extracted from the experimentally observed two-body energies of (1g ₉ ^2/?1 (n) 2d _5/2(n)), (1g ₉ ^2/?1 (n) 1g _9/2(p)) and (1g _9/2(p)-2d _9/2(n)) multiplets in⁹⁰Zr,⁹⁰Nb and⁹²Nb nuclei respectively. Most of the calculated energies and the strengths ofJ ^π=5/2⁺ levels have reasonably good counterparts in the experimental spectrum, however the calculation shows about 17% strength lying at 6.8 MeV, without having a confirmed counterpart in the observed level scheme. The reduced transition strengthsB(M1) forM l transitions from 5/2^? T>(11/2) state to the various components of 5/2⁺ T<(=9/2) state have also been reported; but the corresponding experimental values are not available. The main feature of the reduced transition strengths is that theM1 transition to the state at 3.69 MeV is inhibited whereas that to the state at 6.79 MeV is enhanced, the relevant core-configuration, interfering destructively in the former case and constructively in the latter.     

Effective interactions and charges in58Ni

The structure of the low-lying states of⁵⁸Ni has been calculated in shell model by assuming an inert⁵⁶Ni core plus two valence nucleons in the p_3/2, f_5/2 and p_1/2 orbitals. The two-body matrix elements are first expressed in terms of seven radial matrix elements and these are then parametrized to give best fit between the computed and the observed energies of the levels below 4 MeV. The wave-functions obtained using these two-body matrix elements are used to study the concept of effective charges. It is found that a single effective charge is not sufficient to predict theB(E2) rates equally well for the thirteen known transitions for which experimental values are available. Assumption of state-dependent effective charges gives a far better agreement. An analysis using wavefunctions obtained with Kuo’s two-body matrix elements also gives a similar result.     

Proton-hole states in 115In observed in the 116Sn(d, 3He) reaction

The ¹¹⁶Sn(d, ³He)¹¹⁵In reaction has been investigated at E_d = 50 MeV. Thirteen transitions to states up to 3 MeV excitation energy were studied. The measured angular distributions were compared with DWBA calculations and transferred angular momenta and spectroscopic factors were deduced. Levels at 1.04, 2.23 and 2.52 MeV were found to be excited most likely by l = 3 angular momentum transfer in contrast to previous investigations at lower incident energies in which no l = 3 transitions have been observed.     

A study of the 99Tc(p,d)98Tc reaction

The energy levels of ⁹⁸Tc were studied with the ⁹⁹Tc(p, d)⁹⁸Tc reaction at a bombarding energy of 22.9 MeV and 15 keV resolution (FWHM). The Q-value for this reaction was found to be ?6.755 ± 0.009 MeV and the ⁹⁸Tc mass excess was calculated to be ?86.421 ± 0.011 MeV. This reaction provided the excitation energies for 49 neutron hole states below 1.5 MeV excitation. Comparison of experimental angular distributions with DWBA calculations permitted assignment of lf-values and the extraction of spectroscopic factors for 44 of these levels. Extensive configuration mixing is observed except in the low-lying multiplet. Effective proton-particle, neutron-hole interaction matrix elements were obtained from the low-lying positive-parity multiplet of ⁹⁸Tc.     

The level structure of92Ru up to high spin values

The level structure of⁹²Ru has been studied by means of γ-ray spectroscopy. The nucleus was produced by the⁵⁸Ni(⁴⁰Ca, α2p)⁹²Ru reaction at beam energies of 147 and 187 MeV. The NORDBALL detector system including particle selection was used. A large number of new levels with excitation energies up to 11.3 MeV and spin values up to 22 or 23 units of angular momentum have been established. The level scheme is compared with recent shell model calculations using¹⁰⁰Sn as a core. Some systematics of the g ₉ ^2/?2 configuration is discussed and a strong correlation between the levels in⁹⁰Mo and⁹²Ru is found.     

Comparison of the noncoplanar 6Li(p,pd)4He reactions at 120 and 200 MeV

The ⁶Li(p, pd)⁴He reaction was studied at 200.2 MeV, at the quasi-free angle pair (θ_p, θ_d) = (54°, ?48.9°), for noncoplanarity angles φ from 0° to 28°. ⁶Li αd spectroscopic factors of 0.84 and 0.76 are deduced from our coplanar data at this energy and 120 MeV, respectively, for ground-state 2S Woods-Saxon wave functions. A recent microscopic three-body calculation predicts spectroscopic factors from 0.70 to 0.75; using the ground-state wave functions from this study, we deduce a factor of 0.76 from the 200 MeV data. DWIA calculations fit the measured integrated cross sections versus φ for spectator momenta P_α ? 100 MeV/c at both bombarding energies, but underpredict them for larger P_α. Momentum form factors were better reproduced with 1S αd cluster wave functions for a soft-core bound-state potential than with the 2S Woods-Saxon wave functions, but the former wave functions generate unphysically large (～1.25) spectroscopic factors.     

Depolarization in proton inclusive inelastic scattering and in the (d,p) reaction on medium-weight nuclei

The energy-averaged depolarization parameter K_y^y′ has been measured for the inelastic scattering of 18 MeV protons from ⁵⁴Fe, ⁶³Cu and ⁹²Mo at 45°, 90° and 135°, and for 14.35 MeV protons from ⁶³Cu at 45° and 135°. In all cases K_y^y′ varies from approximately unity for scattering with low energy loss to approximately zero for inelastic scattering to high excitation energies. The change from one of these values to the other occurs over a region ≈ 6 MeV wide centered at about 5 MeV excitation. A simple two-component model fits both the K_y^y′ and inelastic crosssection data. K_y^y′ has also been measured for the ⁵⁴Fe($\text{d}$, $\text{p}$)Fe reaction with 16 MeV deuterons incident. Here K_y^y′ changes from approximately the maximum possible value, $\text{2}\text{3}$, to about zero in a 6 MeV region centered at roughly 13 MeV excitation. The ($\text{d}$,$\text{p}$) data can be fitted by an extension of the model used for the proton scattering data.