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The scattering of [sup 13]C on [sup 13]C and on its mirror nucleus [sup 13]N is considered in the framework of a four-body model with two (inert) [sup 12]C cores and a pair of weakly bound nucleons. Numerical calculations of the elastic angular distributions for the two systems show that the surface transparency of the core-core interaction and the weak binding of the proton in [sup 13]N will enable one to extract the effective neutron-proton interaction from analyses of the [sup 13]C+[sup 13]N elastic scattering.

It was one of Tony Skyrme’s characteristic features to work in close contact with experimental physicists, who interested him in different phenomenological problems. In this way Skyrme was involved in solving the experimental data puzzle, which arose as a result of the fast electron scattering experiments, conducted with the aim of studying the charge distribution within the nucleus (the results werepublished in 1953). As a consequence of those electromagnetic type experiments, as well as from μ-mesonic atoms spectroscopy data or from the isotopic shift data, the value for the radius of the charge distribution within the nucleus was suggested to be $$ \bar R \simeq 1.2A^{1/3} fm $$ (1.1) where, as usual, A is the atomic number. At the same time it was already known from specifically nuclear type experiments such as α-decay, light nuclei reactions, from the penetrability factors calculated for the scattering of neutrons, or from the evidence of the difference in binding energies of mirror nuclei, that one can derive the value for the radius of the nucleus close to $$ \bar R \simeq 1.5A^{1/3} fm $$ (1.2) In combination, these results signified that the electrical charge of the nucleus lies within the radius \( {\bar R} \) but that the specifically nucleonic interactions extend out to the radius R.

Magnetic moments of the A = 12 unstable mirror pair nuclides 12B and 12N have been measured by the β- NMR, technique. The experimentally measured magnetic moments are μ(12B) = 1.001(17)μN and μ(12N) = 0.4571(1)μN The improved shell model using an SFO Hamiltonian with enhanced spin-isospin monopole proton-neutron interaction and modified single-particle energies is employed to calculate the magnetic moments of 12B and 12N. The calculation yields μ(12B) = 0.929μN and μ(12N) = 0.452μN and has produced a new magic number 6 for the short-lived unstable mirror pair nuclides 12B and 12N.

Coulomb displacement energies in mirror nuclei are comparatively analyzed in Dirac-Hartree and Skyrme-Hartree-Fock models. Using a non-linear effective lagrangian fitted on ground-state properties of finite nuclei, it is found that the predictions of relativistic models are lower than those of Hartree-Fock calculations with a Skyrme force. The main sources of reduction are the kinetic energy and the Coulomb-nuclear interference potential. The discrepancy with the data is larger than in the Skyrme-Hartree-Fock case.

Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory. The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus, the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smaller with the increase of the mass number A, and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair of mirror nuclei decrease almost linearly with the increase of the mass number A.

The validity of charge symmetry has long been of fundamental interest and much circumstantial evidence has accumulated over the years favoring charge symmetry breaking (CSB) on the order of a fraction of a percent. Although low energy nucleon-nucleon scattering studies have shown a slight inequality of the nn and pp scattering lengths[1], it has proved very difficult to remove experimental and theoretical uncertainties to isolate charge symmetry breaking interactions unequivocally. Evidence of CSB is present in π scattering from 3 H and 3 He and in π — d total and differential cross section measurements[2],[3],[4],[5]. The π — d results have been interpreted in terms of mass splittings in the Δ system. Differences in the binding energies of mirror nuclei (the Nolen-Schiffer effect) hint at the presence of charge symmetry breaking terms in the interaction but, again, the isolation and removal of electromagnetic (EM) effects has proved difficult[6],[7].

For the first time, we obtained the g factor for the ground state of {sup 23}Al by use of a {beta}-NMR measurement. {sup 23}Al has a small proton separation energy and is a potential proton-halo candidate. The obtained g factor, vertical bar g vertical bar =1.557{+-}0.088, clearly shows the spin and parity, J{sup {pi}}=5/2{sup +}, for {sup 23}Al, which is the same as that of its mirror partner, {sup 23}Ne. The possible nuclear structure of {sup 23}Al is also discussed.

Recent Coulomb shift calculations for the level structure of the $^{20}\mathrm{Na}$ and $^{20}\mathrm{F}$ nuclei predict that the ${3}_{3}^{+}$ state at 2.966 MeV in $^{20}\mathrm{F}$ is the mirror of the 2.646 MeV state in $^{20}\mathrm{Na}$, which is of considerable importance for the reaction rate of $^{19}\mathrm{Ne}$(p,\ensuremath{\gamma}${)}^{20}$Na. Shell model predictions suggest a lifetime of 3.5 fs for the state in $^{20}\mathrm{F}$, in disagreement with the experimentally determined value of 60\ifmmode\pm\else\textpm\fi{}40 fs. The lifetime of low excited states in $^{20}\mathrm{F}$ has therefore been remeasured using the Doppler shift attenuation method (DSAM) and an upper limit of \ensuremath{\le}12 fs for the 2.966 MeV state has been obtained.

Yrast states in mirror nuclei 55Co and 55Ni have been populated with a radioactive ion beam using the Isotope Separator On-Line method. A shielded array of 7 Compton suppressed germanium detectors recorded reaction gamma-rays. For channel selection, an array of 128 independent silicon detectors was used to differentiate exit channels with different number of proton and alpha particles emitted. From gamma-gamma and gamma-particle coincidences, three lines in 55Co and one line in 55Ni was obtained for the first time

The decay of /sub 29//sup 57/Cu/sub 28/ produced with the /sup 58/Ni(p,2n) reaction was identified by a 1112-keV ..gamma.. ray occurring in its daughter nucleus /sup 57/Ni and the half-life and ..beta../sup +/ end-point energy were measured to be 233 +- 16 ms and 7720 +- 130 keV, respectively, applying a technique of fast transportation of irradiated targets. The logft value and Gamow-Teller matrix element of the ground-to-ground mirror transition of /sub 29//sup 57/Cu/sub 28/ (T/sub z/ = -1/2)..-->.. /sub 28//sup 57/Ni/sub 2/ 9(T/sub z/ = 1/2) was deduced to be logft = 3.71 +- 0.05 and = 0.37 +- 0.11. The present results indicate a large reduction of from the single particle value (1.291) although /sup 57/Cu is a nucleus obtained by adding one proton to the /sub 28//sup 56/Ni/sub 28/ core.

Quark mass differences are used to derive an anomalous (i.e., due to the strong interactions) isospin violating potential. The potential includes the effects of pseudoscalar (..pi..-eta-eta') and vector meson (rho-..omega..) mixing. The finite rho width is included. Low energy nn, pp, and np phase shift differences are calculated in terms of the fundamental coupling constants. Despite considerable uncertainty in the coupling constants, it is possible to understand the very small nn and pp scattering length differences. Furthermore, it appears that effects in the l>0 partial waves at finite energies are large enough to be observable in the next few years. Estimates of effects in bound nuclei are presented. These include calculations of the contributions to mirror nuclei binding energy differences and to isospin mixing for a few characteristic cases. In most of those cases the anomalous isospin breaking contributions are of roughly the same size as observed discrepancies. However, inclusion of short range correlations substantially reduces the calculated effects in these cases.

A formalism is presented for extracting isospin mixing in the compound nucleus from a comparison of Ericson fluctuations in the cross section of mirror reactions. Some experimental aspects of the comparison are also discussed.

The mirror nuclei in the f 7/2 shell offer an excellent possibility for systematic studies of various nuclear properties. These nuclei decay by a strong mixed Fermi and Gamow-Teller decay to the ground state of the daughter nucleus and by weak Gamow-Teller decays to the excited states. The accurate determination of the Gamow-Teller strength provides a sensitive test for the nuclear shell-model calculations.

Angular distributions have been measured for six 36 Ar(p, γ ) 37 K resonances in the E p = 0.9−3.0 MeV energy region. These experiments yield spin- and parity assignments to seven excited states of 37 K, γ-ray branching ratios for each state, together with the multipolarity mixing ratios of most transitions. Lifetimes have been deduced from the same data with the DSA method. Excitation energies have been determined with a precision up to 20 eV. A resonance- and excitation-energy measurement at the E p = 918keV resonance yields a 36 Ar(p, γ ) 37 K Q -value of Q = 1857.57 ± 0.09 keV. The 36 Ar(p, p 1 γ ) yield curve, measured in the E p = 2.6–3.3 MeV region, yields additional information on resonance and excitation energies of 37 K states with a typical precision of 0.6 keV. The new data on 37 K levels allow a detailed comparison of the level schemes of the mirror nuclei 37 Ar and 37 K. The present experimental data agree quite well with the results of previous shell-model calculations.

The radiative capture reactions /sup 3/H(p,..gamma..)/sup 4/He and /sup 3/He(n,..gamma..)/sup 4/He are studied within the framework of a microscopic multichannel resonating group model. Employing a charge symmetric nuclear force we find different thresholds for the mirror channels due to the Coulomb force. These differences in term together with channel coupling effects lead to marked variations between observables of the two mirror reactions. We demonstrate that all types of experimental data can be reproduced by our calculation except for the controversial integrated (n,..gamma..) cross section data.

Quadrupole coupling constants of the /sup 43/Sc(19/2/sup -/) and the /sup 43/Ti(19/2/sup -/) mirror isomers, implanted into hexagonal Ti, have been measured with the time differential perturbed angular distribution method. Values of e/sup 2/qQ/h=8.5(19) MHz and 8.0(16) MHz are found at room temperature, corresponding to eQ=19.9(14) efm/sup 2/ and 30(7) efm/sup 2/ for the /sup 43/Sc(19/2/sup -/) and the /sup 43/Ti(19/2/sup -/) states, respectively. The isomeric lifetimes were remeasured as T/sub 1/2/=469(4) nsec and 553(21) nsec for the two states. These values, along with transition rates of high spin states in A=42 nuclei were analyzed in terms of effective charges, and were found to be consistent with e/sub n/=0.56(7) and e/sub p/=1.26(9) for the quadrupole moments, e/sub n/=0.65(3) and e/sub p/=1.35(5) for the B(E2) values. The slight increase in the effective charges for the nondiagonal compared to the diagonal E2 matrix elements is understood as the effect of an increased core deformation in the lower spin partner of the transition.

Angular distributions of the /sup 3/9K(p,t)/sup 3/7K and /sup 3/9K(p,/sup 3/He)/sup 3/7Ar reactions between 3/sup 0/ and 55/sup 0/ have been measured at 40 MeV bombarding energy. The experimental differential cross sections of the transitions to several of the low-lying mirror pairs of even-parity final states in /sup 3/7K and /sup 3/7Ar are compared to results of microscopic distorted-wave Born-approximation calculations based on current shell-model wave functions. The sensitivity of these distorted-wave Born-approximation calculations to optical model parameters is studied.

The excitation functions of the elastic scattering 12C(p, p)12C and the reactions 12C(p, p′)12C (4.44 MeV) and 12C(p, α)9Bg.s. have been measured at θ = 175° in the region of the first T = 3 2 state in 13N with high energy resolution. A straightforward resonance analysis of the elastic scattering data yields Γ = 1.10 ± 0.09 keV, Γp = 210 ± 11 eV and Γ p Γ = 0.191 ± 0.017 . The results are compared with shell-model predictions. The additionally measured angular distributions of the elastic scattering 12C(p, p)12C above and below the resonance are compared with optical model calculations. The combination of the present results for Γp and Γp/Γ with previous results for Γγ/Γp and ΓγΓp/Γ yields Γγ = 27.0 ± 2.2 eV as a new determination of the 13 N (T = 3 2 , 15.07 MeV → T = 1 2 , 0 MeV ) γ-decay width. The comparison with the analogous γ-decay in 13C is discussed with respect to the charge symmetry of corresponding ΔT = 1 γ-transitions in mirror nuclei.

The magnetic moment and lifetime of the first excited states of the mirror nuclei $^{21}\mathrm{Ne}$ and $^{21}\mathrm{Na}$ have been measured by the plunger-time differential-recoil-into-vacuum technique. The states were populated by the $^{4}\mathrm{He}(^{18}\mathrm{O},n)^{21}\mathrm{Ne}$ and $^{10}\mathrm{B}(^{16}\mathrm{O},\ensuremath{\alpha}n)^{21}\mathrm{Na}$ reactions at beam energies such that mainly three-electron recoil ions were produced. Values $|g|=0.28\ifmmode\pm\else\textpm\fi{}0.03$ and $|g|=1.48\ifmmode\pm\else\textpm\fi{}0.10$ have been deduced for the $^{21}\mathrm{Ne}$ and $^{21}\mathrm{Na}$ $g$ factors. The mean lifetimes of these states have been determined as $\ensuremath{\tau}=10.1\ifmmode\pm\else\textpm\fi{}0.3$ ps and $\ensuremath{\tau}=9.9\ifmmode\pm\else\textpm\fi{}0.4$ ps, respectively. The analysis of the measurements also provides information on atomic state populations in two, three, and four electron systems.

Total cross sections and astrophysical $S$ factors of the radiative capture reactions $\ensuremath{\alpha}(^{3}\mathrm{He},\ensuremath{\gamma})^{7}\mathrm{Be}$ and $\ensuremath{\alpha}(t,\ensuremath{\gamma})^{7}\mathrm{Li}$ are investigated by the resonating-group method. The theoretical value of the $S$ factor at ${E}_{\mathrm{c}.\mathrm{m}.}=10$ keV is predicted to be 0.508 keV\ifmmode\cdot\else\textperiodcentered\fi{}b without the use of any artificial parameters. An interesting difference between the mirror reactions is found and theoretically explained.

Many theoretical contributions to nuclear magnetic moments are reviewed with major attention to core polarisation and meson exchange currents. Experimental evidence is drawn from light isobaric mirror nuclei. Relativistic and quark contributions to nuclear magnetic moments are estimated and discussed.

A calculation is made of the mesonic exchange corrections to the allowed axial vector mirror β-decays 15 O → 15 N , 17 F → 17 O , 39 Ca → 39 K and 41 Sc → 41 Ca . It is found that the corrections are significantly state dependent and can be both positive and negative.

In the continuum shell model, the width of the 3/2-, 3/2 resonance state at 15.1 MeV in the mirror nuclei 13C and 13N is calculated. If channel coupling and the Pauli principle are taken into account, the width calculated without external mixing and without isotensor components is of the correct order of magnitude. The calculations show that coupling to isospin-allowed channels which are closed plays an important role.

20 Na ( T 1 2 = 445 ms ) and 36 K ( T 1 2 = 340 ms ) have been produced in rare gas targets by (p, n) reactions and polarized by means of spin-exchange scattering with optically pumped 87 Rb. The asymmetry in the β-decay of polarized nuclei served to detect r.f. transitions between h.f.s. Zeeman levels of the atomic ground states, yielding spins I( 20 Na ) = 2, I( 36 K ) = 2 , and h.f.s. splittings ΔW( 20 Na ) = 276.855(3) MHz , ΔW( 36 K ) = 604.5(1.1) MHz from which the magnetic moments μ I ,( 20 Na ) = 0.3694(2) n.m. and μ I ( 36 K ) = 0.548(2) n.m. (corrected for diamagnetism) were deduced. The magnetic moments are discussed in connection with 20 F and 36 Cl, the mirror nuclei belonging to the same isospin triplets.

The analog of the 4.7-MeV state of the /sup 9/Be nucleus has been observed in its mirror /sup 9/B by the reaction /sup 10/B(/sup 3/He, ..cap alpha..)/sup 9/B(..cap alpha..) /sup 5/Li (g.s.) at E( /sup 3/He) = 2.3 and 5.0 MeV. The excitation energy and width of the state have been deduced. The value of 1.5 +- 0.3 MeV found for the width is in line with the value deduced by the reaction /sup 7/Li(/sup 3/He,n) /sup 9/B, but it is larger by a factor of about 4 than the one measured by the proton following the ..beta../sup +/ decay of the /sup 9/C nucleus.

Cross sections of one- and few-nucleon transfers in the reaction /sup 28/Si+ /sup 28/Si at E/sub lab/ -- 151.25 MeV have been measured with a quadrupole-dipole-dipole-dipole magnetic spectrometer. The one-neutron and one-proton transfers to corresponding shell model states in the pairs of mirror nuclei /sup 29/Si-/sup 29/P and /sup 27/Si-/sup 27/Al are found to be approximately equal. The cross sections for few-nucleon transfers to states with excitation energies E/sub x/

The ${\ensuremath{\beta}}^{+}$ decay of $^{47}\mathrm{Cr}$ (${J}^{\ensuremath{\pi}}$,T${=(3/2)}^{\mathrm{\ensuremath{-}}}$,(1/2)) has been studied following its production by the $^{9}\mathrm{Be}$${(}^{40}$Ca, 2n${)}^{47}$Cr reaction at E${(\mathrm{}}^{40}$Ca)\ensuremath{\approxeq}90 MeV. In addition to the previously reported superallowed decay to the mirror state (i.e., the $^{47}\mathrm{V}$ ground state), we observe a (3.7\ifmmode\pm\else\textpm\fi{}1.2)% allowed ${\ensuremath{\beta}}^{+}$ branch to the ${(5/2)}^{\mathrm{\ensuremath{-}}}$ state at 87 keV in $^{47}\mathrm{V}$. These two branches appear to dominate the decay of $^{47}\mathrm{Cr}$; an upper limit of less than 0.5% is set on possible \ensuremath{\gamma} rays, other than the 87-keV \ensuremath{\gamma} ray, in the range of 15 to 2800 keV. Measurement of the time decay of the 87-keV \ensuremath{\gamma} ray establishes a value of ${T}_{1/2}$=508\ifmmode\pm\else\textpm\fi{}10 ms for the $^{47}\mathrm{Cr}$ half-life which is in significant disagreement with two previously reported values. The present work utilized Ge spectroscopy and a He-jet system for transport of the beam-induced radioactivity, as opposed to previous measurements which used a plastic scintillator to detect positrons and either a He-jet chopper or a slow beam-pulsing system. A summary of decay data for the complete ${f}_{7/2}$ shell series of mirror nuclei is also presented.

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.

A hybrid quark-nucleon model of nuclei is developed in which nucleons merge into multiquark bags at short distances. This model is applied to calculate mass differences between /sup 3/He and /sup 3/H and a number of other mirror nuclei. For light nuclei we obtain a reduction of the discrepancy between experiment and conventional theory. Probabilities for the formation of six-quark bags and nine-quark bags in these nuclei are evaluated, and the consequences of our results are discussed. In particular we comment on the compatibility of conventional and the hybrid quark-nucleon results.

We study the energy systematics in light mirror nuclei of the unbound states having predominant single-particle character. For many levels in the mass range A = 9--17, the observed Thomas-Ehrmann shift is described very well by a simple potential model. We speculate that the missing partner in /sup 9/B of the (1/2)/sup +/ state in /sup 9/Be is observable as a broad continuum with a peak at 0.9 MeV.

States in /sup 47/Cr were studied using the /sup 46/Ti(/sup 3/He,2n) /sup 47/Cr reaction with 22-MeV /sup 3/He ions and the /sup 40/Ca(/sup 12/C,..cap alpha..n) /sup 47/Cr reaction with 38-MeV /sup 12/C ions. Prompt and delayed ..gamma..-..gamma.. coincidence studies were performed. The following decay scheme was established (energies in keV): (15/2)/sup -//sub 1322.3//sup arrow-right/ (11/2)/sup -//sub 1158.3//sup arrow-right/ (7/2)/sup -//sub 75.4//sup arrow-right/ (5/2)/sup -//sub 99.3//sup arrow-right/ (3/2)/sup -/(g.s.). In addition, the (3/2)/sup +/ state was determined to have an excitation energy of 471.5 keV and was found to decay to the (5/2)/sup -/ state. Since /sup 47/Cr has T/sub z/ = (1/2) and is the mirror of the well-known /sup 47/V nucleus, Coulomb displacement energies were deduced. The variation of Coulomb displacement energy with mass number is discussed for f/sub 7/2/ shell nuclei. In addition, we used the measured energies for the first (3/2)/sup +/ states in T = (1/2) mirror pairs of f/sub 7/2/ shell nuclei to determine the average Coulomb interaction energy between a d/sub 3/2/ hole and an f/sub 7/2/ particle, and found an increase in magnitude with increasing mass number.

The Coulomb displacement energy of the mirror nuclei 41Sc-41Ca, 39Ca-39K, 17F-17O and 15O-15N is studied. Shell-model calculations for the ground states are carried out in the 1f721d32 and 1p121d522s12 spaces, considering up to 4p-4h excitations. The configuration mixing effect on the Coulomb energy shift is calculated and the change of the charge radius due to core excitations is taken into account. The effect is particularly important in the calcium region and the Coulomb energy anomaly is decreased in particle nuclei, but increased in hole nuclei. Hartree-Fock calculations using the Skyrme III force are presented and the model dependence on the interaction is discussed in comparison with the HF results of other authors. Other corrections are also taken into account. We finally estimate the discrepancy in the Coulomb displacement energy obtaining approximately, 0.24, 0.50, 0.19 and 0.32 MeV for the above-mentioned mirror nuclei, respectively. These numbers are very similar to the prediction using the charge symmetry breaking potential of Okamoto and Pask.

A systematic study of the core polarization correction to Coulomb displacement energies is carried out. A zero range density independent and density dependent force is used to calculate this correction in the A = 16, A = 40, and A = 208 regions. It is found that the core polarization correction does not increase the Coulomb displacement energies and, therefore, cannot resolve the existing discrepancy between theory and experiment. Moreover, when the mean square radius of the excess neutron distribution is decreased the core polarization correction to the Coulomb energy becomes attractive and cancels the gain resulting from the direct Coulomb term. Hence, it is concluded that the discrepancy cannot be resolved even when the excess neutron distribution has an anomalously small radius. It is also pointed out that when the core polarization term is added the discrepancy is almost equal in mirror nuclei with a single hole in the N = Z core and those with a single particle outside the same core. Evidently, additional charge asymmetric corrections are required to resolve the discrepancies in Coulomb displacement energies.