Search

The ${}^{25}$Mg${(d,}^{3}$He)${}^{24}$Na reaction has been investigated at 29 MeV incident energy. Spectra were measured at ${\ensuremath{\theta}}_{\mathrm{lab}}=10\ifmmode^\circ\else\textdegree\fi{}$ and $18\ifmmode^\circ\else\textdegree\fi{}$. Observations using a split-pole magnetic spectrograph have been made of 56 levels of ${}^{24}$Na in the range of excitation energy between 0 and 7.3 MeV. Most of these have been identified with ${}^{24}$Na levels which have been previously observed by other techniques. From the ratios of the experimental as well as distorted-wave Born approximation (DWBA)-predicted cross sections at the two angles, the population through the pickup of an ${l}_{p}=1$ proton has been established (or confirmed) for the twelve levels at ${E}_{x}=3.372$, 3.745, 3.936, 4.524, 5.192, 5.250, 5.452, 5.846, 5.863, 6.905, 7.084, and 7.246 MeV. Spectroscopic factors were obtained from the comparison of the experimentally measured cross sections at the two angles with the DWBA-predicted cross sections. The experimental values of spectroscopic factors and excitation energies for positive-parity states were compared with the results of a recent, complete $\mathrm{sd}$-shell space, shell-model calculation. In conjunction with the results of various previous works, this comparison leads to the identification of 19 shell-model levels with experimental levels, and thus allows the removal of ambiguities existing in the current literature for the ${J}^{\ensuremath{\pi}}$ values of some ${}^{24}$Na states with ${E}_{x}l$3.7 MeV.

The properties of positive-parity states in 32S are compared to predictions of shell model calculations within the complete s-d basis space using the universal s-d shell Hamiltonian. The experimental T = O spectrum is reproduced to excitation energies between 10 and 11.7 MeV, depending on the level spins. The T = 1 spectrum is known and reproduced for the first five 5 MeV in excitation in general and for the first 8 MeV in the case of Iπ = 1+ states. Altogether the excitation energies of 80 positive-parity states are reproduced with a rms deviation of 200 keV. A calculation of radiative widths and branching ratios for γ-decay which uses effective charges and free-nucleon g-factors yields good general agreement with experiment. The need for effective g-factors is felt only in the rare cases of transitions which are governed by the isovector d3/2 → d5/2 M1 matrix element. The spectrum of negative parity, T = 1 states is understood in terms of the weak-coupling model while that of the T = 0 states is comprised of octupole-quadrupole phonon multiplets. Positive-parity states from outside the s-d configuration are first observed between 9.5 and 10.5 MeV excitation energy.

Assignments of I, π, T are made to 30 levels in 32S between 7.35 and 11.76 MeV excitation energy, making the spectroscopy of the T= 0 states rather complete up to 10 MeV and that of the T = 1 states up to 12 MeV. A reassessment of existing data in the light of the new results clarifies the spectrum of I π = 1+, T = 1 states up to 15 MeV excitation energy. High-spin states (I = 52 - 7) below 10 MeV excitation energy have been investigated by n t γ angular-correlation measurements with the 29Si(α, nγ) reaction at E α 14.4 MeV. Five g-wave resonances of the 31P(p, γ) reaction, leading to the formation of I π + 4+, 5+ states in 32S, have been identified between 10 and 12 MeV excitation energy. The spectrum of T = 1 states between 10.7 and 12 MeV, has been investigated by measurements of γ-ray angular distributions on resonances of the 31P(p, γ) reaction and by measurements of resonance strengths. Several 32S levels between 7.35 and 8.75 MeV excitation energy were studied as final states in resonance decays. Finally a search was performed for I π = 0+ resonances of the 28Si(α, γ) reaction.

Measurements of resonance strengths and ofγ-ray angular distributions or anisotropies have been performed on selected resonances of the25Mg(p, γ) reaction in the rangeEp=2–4 MeV,Ex=8.2−10.1 MeV with an emphasis on high-spin andT=1 analog resonances. EightT=1 states are identified, among them high-spin states at 8747 keV (I=6), 9286 KeV (I=5), and 9986 keV (Iπ = 7+, 6+). Shell model calculations in thes-d basis space reproduce the branching ratios of these states and clarify the nature of final states. New high-spinT=0 states are observed at 9720 keV (Iπ = 7+), 8602 keV (I = 6), and 6695 keV (Iπ = 7+). TheIπ assignments to severalEx = 6–8 MeV states are revised and the role of two-particle excitations into thef-p shell is elucidated. A revised spectrum of 73 positive-parity,T = 0 states is compared to the predictions of shell-model calculations in thes-d basis space using the universals-d shell Hamiltonian.

28Si level scheme up to 14.5 MeV excitation energy is reevaluated using information from two preceding papers. It consists of approximately 250 levels which are almost completely characterized according to the quantum numbersI, π, T of the levels. The properties of positive-parity states are compared to the predictions of shell model calculations within the completes-d basis space using the unifieds-d shell Hamiltonian. A spectrum of 48 experimentalT=1 states between 9.3 and 16 MeV is reproduced with a rms deviation of only 150 keV. A calculation of radiative widths and γ-decay modes which uses free-nucleong-factors yields excellent agreement with experiment and confirms that quenching of M1 transitions is only marginal in28Si. The detailed shell model analysis of theT=0 spectrum is extended to the limiting energy whereT=1 wave function admixtures, not contained in the theory, become important experimentally. This happens at 6–8 MeV above the yrast state, depending on the spin value. Altogether it appears that a spectrum of 171 levels below 14.5 MeV, which have positive or unassigned parity, is almost completely accounted for by the model. Apparent intruder states from outside thes-d shell space are observed atE x =10 945 keV (I π=4+) and 12 860 keV (I π=6+) and are interpreted as members of aK π=0+ rotational band.

New assignments of quantum numbers have been obtained for more than 50 levels in28Si between 8953 and 15915 keV excitation energy. They are based on the measurement of γ-ray angular distributions or anisotropies on 29 resonances of the27Al(p, γ) reaction and on the24Mg(a, γ) resonance atEα=3355 keV. A total of 15 high-spin states withI=5–7 has been obtained and the spectrum ofT=1 states has been identified up to 15915 keV excitation energy and a maximum spinI=6.

The systematics ofγ-decay modes and radiative widths of highly excited states in28Si has been extended by takingγ-ray spectra on 60 resonances of the27Al(p,γ) reaction in the range 1097 keV≤Ep≤ 4492 keV (12643 keV≤Ex≤ 15915 keV) and on the24Mg(α,γ) resonances atEα=3355, 3431, 4003 keV (Ex=12860, 12925, 13 415 keV). Theγ-decay modes of levels in the sub-resonance region (Ex=10−12.5 MeV) were studied with both the27A1(p, γ) reaction and the27A1(d, nγ) reaction at Ed=4,5,6 MeV. Information on radiative widths of levels was obtained by measuring the resonance strengthsSγ=(2I+1)ΓpΓγ/Γ for 52 resonances of the27Al(p, γ) reaction with an emphasis on prospective T=1 states.

We have measured the beta-delayed proton spectrum arising from $^{25}\mathrm{Si}$ produced in the $^{24}\mathrm{Mg}$${(}^{3}$He,2n) reaction. Utilization of a new low-energy proton detector has permitted the observation of protons from 250 to 6000 keV. Most proton groups have been placed into a decay scheme by using penetrability calculations and transitions from the mirror beta decay, $^{25}\ensuremath{\rightarrow}^{25}$Mg. This placement permits the construction of the Gamow-Teller strength function which we compare to a beta strength function calculated from complete-space s-d shell model wave functions.

Inelastic ${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}}$ cross-section measurements at pion incident energies of 150 and 180 MeV were made on ${6}^{\mathrm{\ensuremath{-}}}$ states in $^{24,26}\mathrm{Mg}$. In particular, we have determined the (${\mathit{f}}_{7/2}$${\mathit{d}}_{5/2}^{\mathrm{\ensuremath{-}}1}$${)}_{6}^{\mathrm{\ensuremath{-}}}$ isoscalar ${\mathit{Z}}_{0}$=0.21\ifmmode\pm\else\textpm\fi{}0.02 strength for the strongest T=0, ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${6}^{\mathrm{\ensuremath{-}}}$ state located at 12.11\ifmmode\pm\else\textpm\fi{}0.05 MeV in $^{24}\mathrm{Mg}$, and the isoscalar ${\mathit{Z}}_{0}$=0.17\ifmmode\pm\else\textpm\fi{}0.04 and isovector ${\mathit{Z}}_{1}$=0.21\ifmmode\pm\else\textpm\fi{}0.02 strength for the strongest T=1, ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${6}^{\mathrm{\ensuremath{-}}}$ state located at 9.18 MeV in $^{26}\mathrm{Mg}$. The distorted-wave impulse-approximation pion cross-section calculations required a multiplicative normalization factor of 1.2\ifmmode\pm\else\textpm\fi{}0.1 in order to reproduce the pure isovector strength deduced from electron scattering for the well-known T=1, $^{\mathrm{\ensuremath{\pi}}}$=${6}^{\mathrm{\ensuremath{-}}}$ state at 15.15 MeV in $^{24}\mathrm{Mg}$ and the T=2, ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${6}^{\mathrm{\ensuremath{-}}}$ state at 18.05 MeV in $^{26}\mathrm{Mg}$.

Gamma-decay modes and spin(-parity) assignments of levels in25Mg have been systematically investigated up to 10 MeV excitation energy by particle-γ-ray angularcorrelation measurements with the24Mg(d, pγ) reaction at 6.5 MeV bombarding energy and with the22Ne(α,nγ) reaction at 11.8, 12.5, 14.4 and 15.5 MeV bombarding energy. A level scheme has been established which is comprehensive up to 8.3 MeV excitation energy forI≦9/2 and up to 10 MeV for 9/2

Mean lifetimes of levels in the mirror nuclei 29 Si and 29 P have been measured using the Doppler-shift-attenuation (DSA) method and the reactions 15 N( 16 O, np) 29 Si and 28 Si(p, γ) 29 P. The lifetime values or limits were determined for 14 bound levels in 29 Si below the excitation energy of 9 MeV and for 4 levels in 29 P below the excitation energy of 4.1 MeV. The lifetimes of 5 levels in 29 Si are reported for the first time. In order to provide effective stopping of recoils, the targets were prepared by implanting 15 N and 28 Si into Ta backings. The Monte Carlo method and experimental stopping power were used in the DSA analysis. The experimental transition strengths are compared with recent shell model calculations.

Mean lifetimes of the first 5/${2}^{+}$ and 9/${2}^{+}$ states in the mirror nuclei $^{23}\mathrm{\ensuremath{-}}^{23}$Mg have been measured by application of the Doppler-shift attenuation method and the reactions $^{12}\mathrm{C}$${(}^{12}$C,p${)}^{23}$Na, $^{12}\mathrm{C}$${(}^{15}$N,\ensuremath{\alpha}${)}^{23}$Na, and $^{12}\mathrm{C}$${(}^{12}$C,n${)}^{23}$Mg. The results are 1800\ifmmode\pm\else\textpm\fi{}110 and 1570\ifmmode\pm\else\textpm\fi{}170 fs (5/${2}^{+}$), and 139\ifmmode\pm\else\textpm\fi{}10 and 91\ifmmode\pm\else\textpm\fi{}12 fs (9/${2}^{+}$) for $^{23}\mathrm{Na}$ and $^{23}\mathrm{Mg}$, respectively. For the effective stopping of recoils, the targets were prepared by implanting $^{12}\mathrm{C}$ into Ta backings. The Monte Carlo method and experimentally confirmed electronic and nuclear stopping powers were used in the Doppler-shift attenuation analysis. The experimental transition strengths are compared with the predictions of recent shell-model calculations.

Reported are measurements of angular distributions of resonance-energy positive and negative pions exciting approximately 40 states in {sup 24}Mg and {sup 26}Mg. These include the (ground state, 0{sup +}), (1.36 MeV, 2{sup +}), (4.14, 2{sup +}), (5.93, 4{sup +}), (6.44, 0{sup +}), (7.34), (7.55, 3{sup {minus}}), (8.33, 3{sup {minus}}), (9.32, 4{sup +}), (9.97, 5{sup {minus}}), (11.08, 3{sup {minus}}), (12.06), (13.26), (13.96, 3{sup {minus}}), (15.1, {ital T}=1, 6{sup {minus}}), and (15.4) states in {sup 24}Mg and the (ground state, 0{sup +}), (1.81, 2{sup +}), (2.92, 2{sup +}), (3.59, 0{sup +}), (4.31, 2{sup +}+4{sup +}), (4.90, 4{sup +}), (5.31, 2{sup +}), (5.44, 4{sup +}), (5.69, 4{sup +}), (6.86, 3{sup {minus}}), (7.33, 3{sup {minus}}), (7.79, 3{sup {minus}}), (8.17, 3{sup {minus}}), (9.2, possible 6{sup {minus}}), (10.30, 4{sup +}), and (18.1, {ital T}=2, 6{sup {minus}}) states in {sup 26}Mg. The distorted-wave impulse approximation with a Kisslinger form for the optical potential using a {pi}-nucleon {ital t} matrix at a shifted energy of {minus}25 MeV was found to explain the elastic scattering data from {sup 24,26}Mg in the energy range 116--292 MeV that is spanned by these data. Inelastic distorted-wave impulse approximation calculations employing collective-model deformation parameters were simultaneously fitted to the {pi}{sup +} and {pi}{supmore » {minus}} data for each state.« less

Shell-model calculations are presented for electric quadrupole moments of A = 17-39 nuclei. The shell-model wave functions, which span the complete 0d/sub 5/2/-ls/sub 1/2/-0d/sub 3/2/ model space in all instances, are obtained by diagonalizing an sd-shell Hamiltonian which consists of a fixed single-particle energy spectrum and a single set of two-body matrix elements scaled as a function of the mass number A. Results obtained with harmonic oscillator and Saxon-Woods single-particle radial wave functions and matched effective-charge models are presented for ground states of odd-even and doubly odd nuclei and for J/sup ..pi../ = 2/sup +/ first-excited states of doubly even sd-shell nuclei.

The $^{32}\mathrm{S}$(p,n${)}^{32}$Cl reaction was studied at 135 MeV by the time-of-flight technique. The overall energy resolution obtained was about 270 keV. The forward-angle spectra are dominated by the excitation of ${1}^{+}$ states with characteristic \ensuremath{\Delta}L=0 angular distributions peaked at 0\ifmmode^\circ\else\textdegree\fi{}. The ${1}^{+}$ spectrum is described well by distorted-wave Born approximation calculations with full S-D shell-model wave functions and a normalization factor of 0.60. The strengths of the ${1}^{+}$ excitations are interpreted as being equivalent to Gamow-Teller strengths excited in beta decay. The (p,n) cross sections are converted to reduced transition probabilities, B(GT), by means of a ``universal'' relationship obtained from other nuclei where analog beta decay measurements are available. The general distribution and total strength so obtained are represented well by full S-D shell-model calculations with Gamow-Teller matrix elements adjusted to reproduce the strengths of Gamow-Teller beta decays of S-D shell nuclei. The ${1}^{+}$ (p,n) cross sections are interpreted also in terms of magnetic-dipole (M1) strength and compared with inelastic-electron scattering measurements of such strength in $^{32}\mathrm{S}$. The strength observed in individual states is seen to vary considerably between the two reactions; these differences are ascribed to orbital-current contributions in the electron-scattering reaction not present in the (p,n) reaction. The (p,n) measurements extend to higher excitation energies than the electron-scattering measurements.

The distribution of Gamow-Teller strength in the /sup 18/O(p,n) /sup 18/F reaction was studied at a bombarding energy of 135 MeV. Five 1/sup +/, T = 0 states are identified below E/sub x/ = 7 MeV and a concentration of 1/sup +/ states of presumed T = 1 character is observed between E/sub x/ = 9.5 and 12 MeV. Approximately 82% of the 1/sup +/ strength is concentrated into the ground-state transition and only 5.5% is seen in the T = 1 component. Normalization of the ground-state transition to the known Gamow-Teller matrix element from the analogous beta decay of /sup 18/Ne allows the (p,n) cross sections to be related to the Gamow-Teller strength. The resulting total Gamow-Teller strength observed in the (p,n) reaction is about two-thirds of the minimum value required by the sum rule for a T = 1 nucleus. This result is in reasonable agreement with the total Gamow-Teller strength predicted from a shell-model calculation which uses empirically renormalized single-particle Gamow-Teller matrix elements. The concentration of the T = 0 strength predominantly into the ground state and the observed ratio of T = 1 to T = 0 strength also are consistent with these calculations.

Excitation energies and angular distributions of 26 Al levels in the first 6 MeV of excitation have been measured with the 27 Al(p, d) 26 Al 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.

cap alpha..-particle spectroscopic factors have been calculated in the f/sub 5/2prime/p/sub 3/2prime/p/sub 1/2/ shell model space for transitions from the Ni isotopes to states in /sup 62,64,66,68/Zn. The Zn ground states are found to be described well by weak-coupling /sup 60/Zn/sub g.s./ to the corresponding Ni ground state.

Theoretical E4 transition matrix elements calculated in the full d/sub 5/2/-s/sub 1/2/-d/sub 3/2/ shell-model space are presented for excitations of some ground states of stable nuclei for 18 < or = A < or = 38. These matrix elements have been used to calculate inelastic transition probabilities for electromagnetic and hadronic probes. Available data on the relative magnitudes and energy distributions of E4 excitation strengths are found to be well reproduced theoretically thereby. Based on several experimentally measured transition strengths, the empirical isoscalar E4 effective charge is found to be e/sub p/+e/sub n/2.0=(ts +- 0.2)e. This is similar in magnitude to the analogous isoscalar E2 effective charge, but is much larger than existing theoretical estimates.

The $^{31}\mathrm{P}(^{3}\mathrm{He},d)^{32}\mathrm{S}$ reaction was investigated at 25 MeV incident energy. One-hundred and eleven levels up to an excitation energy of 12.5 MeV were observed using a split-pole magnetic spectrograph. The experimental angular distributions were analyzed with the distorted-wave Born approximation. The optical model parameters used in the distorted-wave Born-approximation calculations were obtained from a fit to elastic $^{3}\mathrm{He}$ scattering data taken on $^{31}\mathrm{P}$ at 25 MeV. Gamow functions were used as form factors for the transferred proton in the case of unbound states. Values of the transferred orbital angular momenta $l$ and spectroscopic strengths were obtained for sixty levels, with many odd-parity levels being observed above 9 MeV excitation. Spin and parity assignments were made upon the basis of the $l$ values obtained from the shapes of the angular distributions and upon comparison with the results of other reactions. Isospin assignments were made by comparison with $^{32}\mathrm{P}$ levels. Except for the ${l}_{p}=1$, $T=0$ transfers, most of the observed spectroscopic strength is concentrated into a few levels. The existence of a $T$-mixed doublet of levels, ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$, is suggested in the 11 MeV region of excitation. The excitation energies and spectroscopic strengths are compared with results of a recent shell-model calculation.

Angular distributions have been measured for 18 levels of $^{19}\mathrm{F}$ populated in the reaction $^{17}\mathrm{O}$($^{3}\mathrm{He}$,$p$) at a bombarding energy of 18 MeV. Within the experimental resolution of 28 keV all levels below 5.7 MeV were observed. Nine states were excited with peak differential cross sections greater than 50 \ensuremath{\mu}b/sr, all others had maximum cross sections of less than 12 \ensuremath{\mu}b/sr. Eight of the nine strong levels are easily identifiable with ${(\mathrm{sd})}^{3}$ shell-model states. The ninth is the state at 5.11 MeV, previously assigned ${J}^{\ensuremath{\pi}}=\frac{5}{{2}^{\ensuremath{-}}}$, but suggested by the present results to have positive parity. Angular distributions were analyzed with the distorted-wave Born approximation. For the strong states, transfer amplitudes were taken from an ${(\mathrm{sd})}^{3}$ shell-model calculation. Agreement in both shape and magnitude is good. Negative-parity hole states and positive-parity core-excited states are very weakly populated, but in many cases, their angular distributions are also well fitted with admixtures of the allowed $L$ values.NUCLEAR REACTION $^{17}\mathrm{O}$($^{3}\mathrm{He}$,$p$), $E=18.0$ MeV; $^{19}\mathrm{F}$ deduced levels, $L$, $\ensuremath{\Pi}$. DWBA analysis.

The lifetime of the lowest 0/sup +/, T = 1 state of /sup 22/Na, which decays 100% to a lower 1/sup +/, T = 0 state, has been measured by the recoil-into-plunger Doppler method. The result, tau = 29.3 +- 1.0 ps, gives the average tau = 28.3 +- 0.8 ps when combined with an earlier result. A comparison of the B(M1) extracted from this lifetime with the Gamow-Teller strength for the analog ..beta.. decay from the ground state of /sup 22/Mg to the same 1/sup +/, T = 0 state in /sup 22/Na shows that the orbital part of the M1 ..gamma.. transition is greatly enhanced relative to the spin part. These results are interpreted in the context of realistic shell-model calculations for sd-shell nuclei.

The reactions 24 Mg(t, p) 26 Mg and 28 Si(t, p) 30 Si have been studied at an incident energy of 18 MeV. Angular distributions have been measured for strongly excited states up to an excitation energy of about 10.5 MeV. A comparison with DWBA calculations using transition amplitudes resulting from a full (sd) shell model calculation generally shows good agreement up to an excitation energy of about 6 MeV, although a few states show significant discrepancies. At higher excitation energies the natural-parity states of the (f 7 2 d 5 2 ) multiplet, and the 2 + and 4 + states of the (f 7 2 ) 2 configuration can be identified in both 30 Si and 26 Mg. The 6 + state is identified in 30 Si, but not in 26 Mg. The expected 0 + states are not clearly identified in either case, although relatively strong transitions with “uncharacteristic” angular distributions are observed near the expected location of these states. DWBA calculations with a (f 7 2 ) 2 form factor suggest that these may in fact be the 0 + states of the (f 7 2 ) 2 configuration.

Coupled-channel Born approximation calculations for the reactions 22Ne(p, t)20Ne and 24Mg(p, t)22Mg to the 0+, 2+ and 4+ members of the ground-state rotational bands have been carried out. The two-nucleon transfer spectroscopic amplitudes were determined from shell-model wave functions, the calculation of inelastic excitations was based on the collective model, and the reaction space was limited to the first 0+, 2+and 4+states in each nucleus. The measured cross sections in the case of 22Ne(p, t) are reasonably well described by this model. However, significant deviations were observed between the calculated cross sections and the experimental data for the 24Mg(p, t) transitions to the 2+ and 4+ states. These discrepancies are possibly attributable to multistep processes involving higher-lying states in 24Mg not included in the reaction space. The effects on the calculations of other possible inadequacies of the reaction model and uncertainties in the parameters of this model are discussed.

Resonant photon scattering from /sup 39/K has been studied with bremsstrahlung produced by electrons with end-point energies of 6.6, 8.5, and 9.4 MeV. Values of gGAMMA/sub 0//sup 2/GAMMA for 24 levels below 9 MeV were measured and the gGAMMA/sub 0/ values of 17 levels were deduced. The widths of some levels above 4 MeV were found to be much larger (on the average, more than a factor of 10) than those reported from experiments using the Doppler shift attenuation method. Three of these levels are known from studies of the (d,/sup 3/He) reaction to carry most of the d/sub 5/2/sup -1/ proton strength in /sup 39/K. The B(M1up-arrow) strength of J = (52/sup +/ levels below 7 MeV is compared with predictions based on simple single-particle shell-model wave functions coupled with free-nucleon and empirically renormalized M1 operators and weighted by single-proton pickup spectroscopic factors.

We have investigated the reaction /sup 18/O(t,p)/sup 20/O using enriched (96.6%) /sup 18/O gas in a rotating gas cell and a multiangle spectrograph. Twenty-two angular distributions were measured for levels up to 10.2 MeV. Results are compared with predictions of a recent shell-model calculation.

The magnetic dipole moments of states in mirror pairs of the $\mathrm{sd}$-shell nuclei and the strengths of the Gamow-Teller beta decays which connect them are compared with predictions based on mixed-configuration shell-model wave functions. From this analysis we extract the average effective values of the single-particle matrix elements of the $l$, $s$, and ${[{Y}^{(2)}\ensuremath{\bigotimes}s]}^{(1)}$ components of the $M1$ and Gamow-Teller operators acting on nucleons in the $0{d}_{\frac{5}{2}}$, $1{s}_{\frac{1}{2}}$, and $0{d}_{\frac{3}{2}}$ orbits. These results are compared with the recent calculations by Towner and Khanna of the corrections to the free-nucleon values of these matrix elements which arise from the effects of isobar currents, mesonic-exchange currents, and mixing with configurations outside the $\mathrm{sd}$ shell.RADIOACTIVITY $A=17\ensuremath{-}39$ nuclei, magnetic dipole moments and Gamow-Teller beta-decay strengths; shell-model wave functions, complete $0\ensuremath{\hbar}\ensuremath{\omega}$ $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ basis space, empirical Hamiltonian; extraction of empirical normalizations of the $l$, $s$, and ${[{Y}^{(2)}\ensuremath{\bigotimes}s]}^{(1)}$ single-particle operators.

The Gamow-Teller beta-decay transitions of $\mathrm{sd}$-shell nuclei with five or more excess neutrons are calculated from complete ($0{d}_{\frac{5}{2}}, 1{s}_{\frac{1}{2}}, 0{d}_{\frac{3}{2}}$) space shell-model wave functions. These wave functions are obtained from diagonalizations of a model Hamiltonian formulation which reproduces observed energy-level structures throughout the $\mathrm{sd}$ shell. The calculations are carried out with both the "free-nucleon" normalization for the Gamow-Teller single-nucleon matrix elements and one based on the empirical values obtained for these quantities from a comparison of corresponding theoretical and experimental Gamow-Teller magnitudes near the line of stability. The phase-space factors $f$ which connect the reduced Gamow-Teller strengths to the total half-lives and the individual decay probabilities are calculated both from the energies obtained in the shell-model calculations and, alternatively, from hybrid energy spectra in which available experimental energies are substituted for the corresponding calculated values wherever possible. Comparisons of the beta-decay predictions to existing experimental results are presented and discussed.RADIOACTIVITY Predictions of total half-lives and decay probabilities to individual daughter states of the isotopes of O, F, Ne, Na, Mg, Al, Si, and P which have neutron excesses of five and greater; shell-model calculations, complete $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ basis space, empirical $\mathrm{sd}$-shell Hamiltonian.

Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the 1p32, 0f52 and 1p12 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.

Theγ-decay of levels in21Ne up to 10 MeV excitation energy has been investigated byn — γ coincidence measurements initiated with the18O(α, nγ) reaction at 12, 13, 14.5 and 15.4 MeV bombarding energies. Spin(-parity) assignments of excited states are obtained by combining then — γ angular correlation measurements performed atE α=11, 11.82 and 13.6 MeV with a consideration of lifetimes, neutron penetrabilities of the unbound states, and information from the mirror nucleus21Na. The resulting values of Ex[keV]−J π are as follows: 4525-5+, 4686-3+, 5431-7+, 5549-3+, 5819-7−, 6175-7+, 6268-9+, 6550-9, 6639-9, 7006-7+, 7041-9, 7356-7 or 9, 7422-11(−), 7648-7+, 7981-11 or (7+), 8154-9, 8240-11, 8664-9− or 11 or 13−, 9401-13−, 9867-13− or 15+, 9941-13− or 15 or 17+. The assignment of mirror levels in21Ne —21Na has been extended to the 6175 keV level of21Ne. Excitation energies, electromagnetic properties, Gamow−Teller matrix elements and spectroscopic factors of positive parity states are compared with the results of shell-model calculations which employ a unifieds—d shell Hamiltonian and the unrestricted configuration space of the 0d 5/2 —1s 1/2—0d3/2 shell. Collective properties contained in shell model wave functions are explored up to the termination of bands atJ=17/2 or 19/2. The spectrum of intruder states in21Ne is observed to begin with a 5628 keV,J π=7/2+ state. The 7422, 8664 and 9401 keV levels are assigned as members of previously established negative-parity rotational bands.

In this review we concentrate on recent results of shell model calculations and related experimental data obtained for the sd-shell nuclei. Model spaces and effective interactions, Gamow-Teller, magnetic dipole, electric quadrupole, and higher multipole matrix elements, and electron scattering form factors are discussed. (AIP)

Mean lifetimes of levels in 24Mg have been measured using the Doppler-shift-attenuation (DSA) method in conjunction with the reactions 23Na(p, γ)24Mg and 12C(14N, pn)24 Mg. The lifetime values or limits were determined for 27 bound levels below the excitation energy of 11 MeV; the lifetimes of 3 levels are reported for the first time. For the effective stopping of recoils, the targets were prepared by implanting 23Na and 12C into Ta backings. The Monte Carlo method and the experimental stopping power were used in the DSA analysis. The experimental transition strengths are compared with recent shell-model calculations.

The experimental angular distributions of several multinucleon transfer reactions induced by /sup 18/O on /sup 28/Si have been measured and compared with distorted-wave reaction calculations. The shape and relative intensities of the data can be reproduced by theoretical calculations which seem to open the way for this type of study of structure of nuclei in the middle of the 2s-1d shell. On the other hand, we have not found it possible either to reproduce the shapes of the angular distributions with an optical potential derived from an elastic scattering analysis or to correctly calculate the absolute values of the cross sections. These difficulties which are similar to those encountered in other heavy-ion reaction studies will require extended improvements in the current formulations of the theory for the reaction processes.

The reaction /sup 21/Ne(/sup 3/He,p) /sup 23/Na has been investigated at a bombarding energy of 18.0 MeV, using enriched /sup 21/Ne gas contained in a rotating gas cell. Angular distributions for the positive-parity states have been analyzed with the distorted-wave Born approximation, using transfer amplitudes from an (sd)/sup 7/ shell-model calculation. Agreement with experiment is good. Tentative correspondences are suggested for all experimental and theoretical levels below 6 MeV excitation. Low-lying negative-parity states are very weakly populated.

cap alpha..-decay data from nuclei with 17 < or = A < or = 39 are analyzed with full sd-space shell-model wave functions to determine the effective values of the single-particle matrix elements of the Gamow-Teller operator between all combinations of sd-shell orbitals.

A detailed study of the results of correcting BCS approximation for the effects of particle-number projection and blocking has been carried out. A low-seniority shell-model approximation was used as the frame of reference for investigating the mixing of one- and three-quasiparticle states in odd-mass Ni isotopes and in odd-mass N = 82 isotones. We discuss the results obtained for the energy spectra and electromagnetic decay properties. Effects of seniority-five configurations on the low-lying states have also been studied through the comparison of the low-seniority shell-model results with those which arose from the corresponding full shell-model calculations.

Ground-state binding energies and excited-state energies of nuclei in the 1s-Od shell are analyzed in terms of a variety of two-body interactions. In addition to simple interactions such as the delta and surface-delta, we consider potentials of the finite-range, one-boson-exchange type for the central, tensor, and spin-orbit components of the interaction, with multipole terms added to the central part. The relative importance of these components, together with that of the antisymmetric spin-orbit component, is considered. The antisymmetric spin-orbit component is found to be the least important. Both density-dependent and density-indpendent interactions are considered. Our results favor a density-dependent form for the central and spin-orbit components. We develop a semi-empirical “best-fit” interaction based on a 14-parameter density-dependent two-body potential which reproduces 447 sd-shell binding-energy data to within an rms deviation between experiment and theory of 260 keV. This semiempirical interaction is compared to typical G-matrix interactions as well as to the purely empirical interactions obtained by using two-body matrix elements or Talmi integrals as parameters of the fit.

Analysis of the magnetic dipole moments and the elastic magnetic electron scattering form factors of the 1 2 + ground states of 19 F, 29 Si and 31 P demonstrates that the momentum transfer dependence of the data can be understood in terms of a q -independent M1 operator in combination with the effects of configuration mixing within the space of sd-shell orbits.

We present arguments which indicate the Gloeckner-Lawson prescription for eliminating states with spurious center-of-mass motion from highly truncated shell-model calculations is not generally useful.

Angular distributions of the 29Si(3He, p)31P reaction at E 3 He = 26 MeV have been measured for states in 31P up to an excitation energy of 5.7 MeV. These data were analyzed with distorted-wave Born approximation calculations based on current shell-model wave functions.

Excitations of a $T=0$ and nine $T=1, {1}^{+}$ states have been observed in the reaction $^{28}\mathrm{Si}(p,{p}^{\ensuremath{'}})$ at 201 MeV. The magnitudes of the measured cross sections of the isoscalar and isovector transitions are, respectively, about 24% and 33% of predictions obtained with fullbasis $\mathrm{sd}$-shell-model wave functions. The large reduction factor in the isoscalar channel, where $\ensuremath{\Delta}$-isobar effects must be insignificant, suggests that higher-order configuration mixing must be an important source of quenching in both isoscalar and isovector channels.

New high spin states in 25Mg have been located above the neutron threshold using the 12C(14N, pγ)25Mg reaction at E=23.5 MeV. The members of the ground state rotational band (Kπ=52+ have been tentatively identified up to 152+. The yrast 152+ (not a member of the ground state band) and 172+ states have also been tentatively assigned. These results support the interpretation of the new 172+ state and the previously known yrast 132+ state as fully aligned prolate configurations, i.e., prolate particle-hole states with K=I and γ=-120°.

The (3He, n) reaction has been studied on targets of 20Ne, 24Mg, 32S and 36Ar at 25.4 MeV using a time-of-flight spectrometer. Angular distributions were measured for neutron groups up to excitation energies ranging from 8.55 MeV in 22Mg to 7.47 MeV in 38Ca. New levels were found at 6.98 ± 0.08, 7.84 ± 0.09, 8.29 ± 0.04 and 8.55 ± 0.09 MeV in 22 Mg ; 5.62 ± 0.03 and 6.99 ± 0.05 MeV in 34 Ar ; and 7.47 ± 0.05 MeV in 38 Ca . DWBA analysis along with comparisons with results of (t, p) studies on the same targets permits a number of new spin-parity assignments. Comparison with results of (sd) shell model calculations shows generally good agreement for 22Mg and 26Si up to excitation energies of about 5 MeV. At higher excitation, transition strengths show the increasing importance of (fp) shell contributions. Results for 34Ar show significant deviations from model predictions for most excited states. For 38Ca, only the ground state transition shows appreciable strength for (sd) transfer. In all nuclides strong transitions to negative parity states are observed, and (fp) contributions to measured cross sections become important for even parity states at high excitation.