E2 core polarization for sd-shell single-particle states calculated with a skyrme-type interaction

We have studied the core-polarization effect on the 1s0d-shell single-particle electromagnetic quadrupole transitions due to coupling with the quadrupole giant resonances. The self-consistent Hartree-Fock + RPA method is applied for the calculations of the single-particle wave functions and the response functions of the giant resonances. The particle-vibration-coupling model is used to calculate the core-polarization effect in the vicinity of ¹⁶O and ⁴⁰Ca. The effective coupling hamiltonian is determined by the SGII Skyrme-type interaction which is used in the HF + RPA and particle-vibration-coupling calculation. The results are discussed for the proton and neutron effective charges and for the longitudinal and transverse form factor for the $\text{0}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{→ 1}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ pro single-particle transition in ³⁹K. Good agreement with recent longitudinal data for this transition is obtained.     

The level structure of 187Os

A study of the level structure of ¹⁸⁷Os has been performed by means of (d, p), (d, t) and (d, d$\text{)}\text{?}$ reactions. Based upon the data presented and information available from the 10.5 h decay of ¹⁸⁷Ir, a level scheme including several new states and level assignments is proposed. The low-lying rotational bands built on the $\text{1}\text{2}{}^{\mathrm{?}}$ [510] and the $\text{3}\text{2}{}^{\mathrm{?}}$ [512] single-particle states have been analysed by means of Coriolis-coupling calculations including attenuations of the coupling matrix elements. The calculations involve fits to energies, to neutron transfer cross sections and to ratios of B (E2) values.     

Velocity dependence of the nucleon-nucleon interaction,exchange currents and enhancement of the dipole sum rule in nuclei

A model is employed to describe the velocity dependence of the effective nucleon-nucleon interaction in nuclear matter. The interactions in this model consist of π^? and ρ-meson exchange, together with short-range correlations induced by the strongly repulsive potential resulting from ω-meson exchange. With known coupling strengths, these interactions produce an effective mass $\text{m}{}^1\text{/m = 0.75}$ in nuclear matter.Through the formalism of Fermi liquid theory, the exchange-current correction to the orbital g-factor, δg_l, can be described in terms of the velocity dependence in the neutron-proton interaction, and, within the model, this can be related to the effective mass $\text{m}{}^1$. With $\text{m}{}^1\text{/m = 0.75}$, the δg_l for the proton turns out to be 0.22, 45% of it coming from π-meson exchange.Additional contributions to $\text{m}{}^1\text{/m}$ in nuclei come from the coupling of vibrations to quasiparticles; these are especially important in the nuclear surface, and tend to increase the effective mass, when averaged over both nuclear volume and surface, so that $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{? 1}$. In so far as these contributions arise from isovector vibrations, we can use the same model as for π- and ρ-meson exchange, and show that the same relation between $\text{m}{}^1\text{/m}$ and δg_l holds, so that for $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{= 1}$, δg_l = 0. The contributions from coupling to vibrations will depend upon the single-particle state, however; states of high-angular momentum will tend to have $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{< 1}$ and δg_l > 0.Finally, the enchancement δg_l in gl can be connected with the enhancement k in the dipole sum rule originating from the giant-resonance region. This connection is not very precise, but gives a small positive κ ～ 0.2.     

The quasihole aspect of hole strength distributions in odd potassium and calcium isotopes

The ${}^{\mathrm{40,42,44,48}}\text{Ca}\text{(}\text{d}\text{, ρ)}{}^{\mathrm{39,41,43,47}}\text{K and}{}^{\mathrm{40,44}}\text{Ca(d, t)}{}^{\mathrm{39,43}}$ reactions have been studied at 52 MeV. Angular distributions have been taken and spectroscopic factors have been extracted by means of a DWBA analysis for states with excitation energies up to typically 10 MeV. Analog relations are proposed for mass-39 and mass-43 nuclei. A discussion of proton occupation numbers for various shells above and below the Fermi surface shows a substantial and about equal core excitation for ⁴²Ca and ⁴⁴Ca. Typically 70 % of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ hole strengths have been located. The corresponding energy averaged strength distributions show quasihole structures whose widths are dominated by phonon-hole coupling to the first 2⁺ state in the target nucleus.     

Leptonic decays of the Ω−

Branching ratios, widths, and lepton energy spectra are derived for the leptonic decays of the $\text{Ω}{}^{\mathrm{?}}$ into β⁰ and $\text{β}{}^{01}$. The calculations are made by hypothesizing that higher-order multipoles in an expansion of the baryon current are zero. The axial vector coupling is determined using the bag model.     

Radiative transitions and the P wave levels in charmonium

A value of $\text{1}\text{2}$ or less for the ratio $\text{[E(2}{}^{\mathrm{++}}\text{) ? E(1}{}^{\mathrm{++}}\text{)]}\text{[E(1}{}^{\mathrm{++}}\text{) ? E(0}{}^{\mathrm{++}}\text{)]}$ of the P level splittings in approximate agreement with the assignment of the states at 3.41, 3.50 and 3.55 to the 0⁺⁺,and 2⁺⁺ P-wave levels, is obtained with a short-range Coulomb (Lorentz vector) potential together with a long-range linear (Lorentz scalar) confining potential. The radiative transition widths Γ(ψ′ → 3.41 + γ), Γ(ψ′ → 3.50 + γ), Γ(χ′ → 3.55 + γ) are significantly smaller than those obtained in previous (one-channel) charmonium calculations. The best results were obtained by allowing the Coulomb coupling constant α_s to have a momentum dependence suggested by asymptotic freedom formulae.     

Evidence for two-step processes in reactions with spherical nuclei

Experimental evidence for two-step processes in reactions with spherical nuclei is obtained from a study of ⁵⁴Fe(p, d)⁵³Fe angular distributions for low-lying $\text{9}\text{2}{}^{\mathrm{?}}$ and $\text{11}\text{2}{}^{\mathrm{?}}$ states. Predictions of the coupled-channel Born approximation give excellent agreement with the data.     

The 152,154Eu(t, α) reactions: Studies of the 112[505] bands in 151Sm and 153Sm

Radioactive targets of ¹⁵²Eu(13 y) and ¹⁵⁴Eu(8.5 y) have been used to study the ^152,154 Eu(t, α)^151,153Sm reactions at an incident triton energy of 16 MeV. In these studies, we have identified the bandhead and three excited rotational states of the $\text{11}\text{2}\text{[505]}$ neutron orbital in both the ^151,153Sm nuclei The angular distributions and relative intensities for states in this band in both ^151,153Sm are reproduced reasonably well by using DWBA calculations and by assuming strongly deformed single-particle wave functions. We have used our results and the results of other studies to determine the equilibrium prolate shapes of both ^151,153Sm when the odd-neutron quasiparticle occupies the $\text{11}\text{2}\text{[505]}$ orbital. We estimate $\text{β}{}_2\text{~ 0.26}\text{for}{}^{151}\text{Sm and}\text{β}{}_2\text{~ 0.3}\text{for}{}^{153}\text{Sm}$.     

Giant spin-isospin vibrations and the continuum spectra from the (p,n) reaction at forward angles

The giant Gamow-Teller (GT) resonance and the spin-isospin multipole vibrations are calculated in terms of the continuum RPA. The effective particle-hole interaction consists of the Migdal parameter $\text{g′ = 0.7 (}\text{in units of}\text{?;}{}^2\text{μ}{}_{\mathrm{\pi }}{}^2\text{≈390}\text{MeV}\text{·}\text{fm}{}^3\text{)}$ and the one-pion exchange potential. The RPA response functions are obtained within the full 1p-1h space. In addition to the natural escaping width of the single particle, a constant spreading width for 1p-lh states is incorporated into the correlation function, which makes numerical calculations fast and feasible. The giant GT resonances in ⁹⁰Zr and ²⁰⁸Pb collect, respectively, about 80% and 93% strengths of the sum-rule limit within the nucleon degrees of freedom. It is found that the strengths are further quenched by about 30% due to the coupling with the isobar Δ(1230)-hole configuration. The total quenching thus amounts to 0≈45% and ≈40% respectively in two cases, which is in fair agreement with experiment. The continuum cross section of the ⁹⁰Zr(p, n) reaction at forward angles are calculated for spins up to J = 4 with both parities in the distorted-wave Born approximation. While the giant GT resonance is located at a low excitation energy $\text{h}\text{?}\text{ω ≈ 17}\text{MeV}$, the broad peaks of the dipole and quadrupole modes are found to dominate at $\text{h}\text{?}\text{ω ≈ 25}\text{and}\text{35}\text{MeV}$, respectively. The calculation fairly reproduces the experimental inclusive cross sections up to $\text{h}\text{?}\text{ω ≈ 50}\text{MeV}$.     

The effects of finite range and channel coupling in the 32S(3He, 4He)31S reaction

Comparisons of exact finite-range (EFR) DWBA calculations and zero-range (ZR) calculations are presented for the cross sections and analysing powers of the ${}^{32}\text{S}\text{(}{}^3\text{He}\text{,}{}^4\text{He}\text{)}{}^{31}\text{S}$ reaction to the ground state ($\text{1}\text{2}{}^{\mathrm{+}}$), $\text{1.25}\text{MeV}\text{(}\text{3}\text{2}{}^{\mathrm{+}}\text{)}\text{and}\text{2.23}\text{MeV}\text{(}\text{5}\text{2}{}^{\mathrm{+}}\text{)}$ states. The data for the $\text{3}\text{2}{}^{\mathrm{+}}\text{and}\text{5}\text{2}{}^{\mathrm{+}}$ states are quite well fitted and show the characteristic j-dependence of the analysing powers. Only small differences between the EFR and ZR calculations are seen. The analysing power data for the $\text{1}\text{2}{}^{\mathrm{\pm }}$ state are poorly fitted by the EFR or ZR calculations but better agreement is obtained when the coupling to other levels is included in a coupled channel Born approximation (CCBA) calculation.     

3Σu−-3Σu+ coupling in the O2B3Σu− predissociation

The role of $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ spin-orbit mixing in the O₂ Schumann-Runge predissociation is investigated. The $\text{2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state is found to cross the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state near 2.0 Å with an interaction matrix element of approximately 55 cm^?1. This state contributes to the widths of the Bv ≥ 6 levels, but introduces only small level shift perturbations. When the partial widths due to the ${}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ interaction are added to the previously calculated widths due to the ⁵Π_u, ³Π_u, and ¹Π_u states, reasonable agreement is obtained with experimental measurements on O¹⁶O¹⁶ and O¹⁸O¹⁸. The possibility of non-Lorentzian line profiles and the dependence of the width on rotational quantum number is investigated. The approximation of the spin-orbit matrix element by its value at the crossing point is shown to be a good approximation for calculating the second difference perturbations.     

An energy-independent nonlocal potential model. II. The asymmetry term

We analyze the single-particle bound-state properties and the elastic scattering of protons and neutrons in various groups of isotopes, ranging from C up to Sn, by means of an energy-independent nonlocal optical model. The potential is obtained as an extension of the one used in the analysis of N = Z nuclei, the new term being a Lane-type potential with the same geometrical parameters as the isoscalar one. The radius of the potential is determined by the fit of single-particle energies and charge distribution in one nuclide of each group and it is given by $\text{R}{}_{\mathrm{N}}\text{= 1.16 (A?1)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{F}$. The well depths of the equivalent local potential are fitted to a large set of single-particle energies, measured in stripping and pick-up reactions, and show an energy dependence which is consistent with a unique nonlocal energy-independent potential having isoscalar nonlocality $\text{β ? 1F}$ and isovector nonlocality $\text{β}{}_{\mathrm{T}}\text{? 1.6F}$. In particular, the bound-state data can determine the isovector part of the potential with fair accuracy, provided that proton and neutron, T> and T<, particle and hole states are analyzed: its average value at zero energy shows an increasing behavior from C to Mo. The nucleon point distribution and r.m.s. radii corresponding to this model potential have been calculated in various nuclei.     

Gamma decay of particle-core states in 209Pb

A γ-decay scheme for levels in ²⁰⁹Pb up to 4.13 MeV of excitation has been established by means of the reaction ²⁰⁸Pb(d, pγ)²⁰⁹Pb. In high efficiency p-γ coincidence measurements γ-cascades have been observed from the single-particle states and from core-excited states with very small single-particle strength. Assuming a qualitative validity of the weak-coupling model spins and main configurations of particle-core states can be deduced from their γ-decay. The $\text{J}{}^{\mathrm{\pi }}\text{= (}\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{5}\text{2}{}^{\mathrm{?}}\text{or}\text{7}\text{2}{}^{\mathrm{?}}\text{,}\text{11}\text{2}{}^{\mathrm{?}}\text{,}\text{15}\text{2}{}^{\mathrm{?}}\text{)}$ members of the $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{?3}{}^{\mathrm{?}}$ multiplet could be located. A systematic manner of doublet splitting is found for the lowest states with main configuration $\text{(}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{?3}{}^{210}\text{Pb}\text{(0}{}^{\mathrm{+}}\text{, 2}{}^{\mathrm{+}}\text{, 4}{}^{\mathrm{+}}\text{, 6}{}^{\mathrm{+}}\text{, 8}{}^{\mathrm{+}}\text{)}$. A new decay branch of the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ single-particle state is attributed to an admixture of quadrupole core vibration.     

Formation of covalent nuclear molecules in the 13C + 12C system

Angular distribution's of the elastic scattering of ¹³C on ¹²C and the inelastic scattering leading to the lowest-lying $\text{1}\text{2}{}^{\mathrm{+}}$ and $\text{5}\text{2}{}^{\mathrm{+}}$ states in ¹³C have been measured at energies close to the Coulomb barrier. Analyses carried out in the framework of a complete coupled-reaction-channel theory show that extremely polarized single-particle molecular orbits (hybridization) are formed during the scattering process which give rise to a multiple-step interaction of the valence nucleon, i.e. the formation of a covalent nuclear molecule.     

Core polarization for M2 transitions in odd-A tin isotopes

The reduced M2 transition probabilities $\text{11}\text{2}{}^{\mathrm{?}}{}_1\text{→}\text{7}\text{2}{}^{\mathrm{+}}{}_1$ in the odd-A isotopes ^109–121Sn are found to reveal a specific behaviour. B(M2) values are calculated in the framework of the quasiparticlephonon model. The coupling of a quasineutron with the 2⁺, 3^? and 2^? one-phonon core excitation is taken into account. Inclusion of all one-phonon 2^? states up to 24 MeV in the wave functions of the excited states $\text{11}\text{2}{}^{\mathrm{?}}{}_1\text{and}\text{7}\text{2}{}^{\mathrm{+}}{}_1$ reduces the theoretical B(M2) values by 3–4 times as compared to the single-particle values. The specific B(M2) dependence on the mass number appears to be due to the pairing effect.     

Systematics of nn states with high spin: A study of the (α, 2He) reaction on fp shell nuclei

At 57 MeV bombarding energy the (α, ²He) reaction has been investigated on targets of ^54,56Fe, ^58,60,62,64Ni, ^64,66Zn, and ⁷⁰Ge. Selective excitation of the 2n configurations $\text{(}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{7?}}$, , and $\text{(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{6+}}$ was observed in all final nuclei. A linear A and T dependence of the binding energies of these states was observed. This systematic behaviour is well described by the Bansal-French model. The values obtained for the strength of the isoscalar and the isovector parts of the particle-hole interaction are consistent with the average of the values describing the corresponding single-particle states.