Calculation of spectroscopic amplitudes using boson expansion wave functions

A formalism is derived which allows the evaluation of spectroscopic amplitudes for two-nucleon transfer reactions. The transfer is assumed to take place between low-lying collective states described by boson expansion wave functions. Numerical calculations have been performed for (t, p) reactions on^{148, 150, 152}Sm. Excellent agreement is obtained for cross sections leading to the ground state in the residual nucleus.     

How crossing affects the analytic relationship between low energy ππ amplitudes and their asymptotic behaviour

Different physical assumptions about the asymptotic behaviour of ππ amplitudes are realised in the different number of substractions involved in fixed t dispersion relations for the various amplitudes and their inverses. The fact that each new dispersion relation must be consistent with s - t crossing leads to a number of conditions relating low energy ππ amplitudes to their high energy behaviour. These are discussed in detail. Such relationships supplement finite energy sum rules with which they are compared. The dispersive sum rules, crossing conditions, and finite energy sum rules we discuss are applied to recent phenomenological solutions to Roy's equations and shown not to narrow the presently accepted range of threshold parameters. These results are in marked contrast to the conclusions of other recent studies. To complete the study of finite energy sum rules we consider the behaviour of the isospin zero t-channel amplitude and estimate the asymptotic ππ total cross-section. We present evidence to suggest that the pomeron is late-developing in meson-meson scattering.     

Multipole moments and spin-dependent sum rules and their applications to f72 and s-d shell nuclei

Matrix elements of multipole operators, defined separately for neutrons and protons, are related to spin-dependent sums of spectroscopic factors. A clarification of their relation to the matrix elements of single-particle operators enables the overlap representation to be formally extended to a stripping form for J ≠ 0 operators. Multipole moments obtained from $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ transfer data are found to be dominated by the quadrupole moments when the final nucleus is odd-odd.A previously found (2J + 1) rule for spectroscopic sums, which arises when the odd-J multipole moments vanish, is shown to lead to approximate sum rules which apply separately to stripping and pickup data. The sum rules are generally well satisfied for transfers leading to odd-odd nuclei in the s-d shell.     

Observables for the even type of nucleon in the ground states of odd-mass nuclei

Existing data for lighter nuclei on observables, including magnetic moments and single particle multiple moments, are explained if the even nucleons are predominantly coupled to spin zero but with a substantial spin-2 wave function component. Strong predictions can be made on the basis of such wave functions regarding spectroscopic sum rules and the behaviour of general observables such as B(EL) transition rates.     

Amplitude analysis of Kaon-nucleon scattering data

The KN scattering amplitudes have been extracted from experimental data in the energy range 3 ? k ? 14 GeV/c and for transfer values between ?0.05 and ?0.6 GeV².The ω and P+f helicity-flip amplitudes and the A₂ helicity non-flip amplitude have been neglected; it is shown, that these simplifications are compatible with the data and have no significant influence on our results. One needs to assume the approximate validity of SU(3) symmetry for the ? and A₂ couplings. A very important constraint for this analysis comes from recent experimental data for the reaction K_L⁰p → K_S⁰p. The results for A₂ and ω exchanges are analysed as functions of momentum transfer and energy and we test several current theoretical ideas. Information about f-exchange is also obtained when some further assumptions are made concerning SU(3) symmetry and duality at t = 0. Extrapolating the amplitudes to t = 0 a comparison is made with dispersion relation calculations; at other t-values we compare with results obtained from finite energy sum rules and other analyses based on fixed f analyticity. The predictions for KN data which have not been considered in this analysis are shown to be in good agreement. One of our results is that the ?-ω universality rule is approximately satisfied; we also find a strong indication for a peripheral behaviour of the imaginary part of the non-flip f-exchange amplitude.     

Test of sum rules in nucleon transfer reactions

The quantitative consistency of nucleon transfer reactions as a probe of the occupancy of valence orbits in nuclei is tested. Neutron-adding, neutron-removal, and proton-adding transfer reactions were measured on the four stable even Ni isotopes, with particular attention to the cross section determinations. The data were analyzed consistently in terms of the distorted wave Born approximation to yield spectroscopic factors. Valence-orbit occupancies were extracted, utilizing the Macfarlane-French sum rules. The deduced occupancies are consistent with the changing number of valence neutrons, as are the vacancies for protons, both at the level of <5%. While there has been some debate regarding the true "observability" of spectroscopic factors, the present results indicate that empirically they yield self-consistent results.     

Excitation of lowest 0+-states in two-neutron transfer reactions in even actinides

The spectroscopic factor is considered for two-nucleon transfer reactions involving the excitation of quadrupole one-phonon states. The particle number conservation condition for the collective phonon state is chosen in the form of the adiabatic theories with the moving frame. The variation of the energy gap in the collective phonon state is taken into account as well as the difference of the mean numbers of particles in the initial and final nuclei. Numerical calculations of the spectroscopic factor are carried out for the (p, t)- and (t, p)-reactions for a number of actinide nuclei.     

Electronuclear sum rules

Generalized sum rules are derived by integrating the electromagnetic structure functions along lines of constant ratio of momentum and energy transfer. For non-relativistic systems these sum rules are related to the conventional photonuclear sum rules by a scaling transformation. The generalized sum rules are connected with the absorptive part of the forward scattering amplitude of virtual photons. The analytic structure of the scattering amplitudes and the possible existence of dispersion relations have been investigated in schematic relativistic and non-relativistic models. While for the non-relativistic case analyticity does not hold, the relativistic scattering amplitude is analytical for time-like (but not for space-like) photons and relations similar to the Gell-Mann-Goldberger-Thirring sum rule exist.     

Core exchange symmetries in heavy ion reactions

The general symmetry properties of theT-matrix due to the exchange of identical cores in nuclear reactions between composite particles are given. For the case of direct transfer reactions an explicit expression for the cross section is derived in the distorted wave Born approximation. In this model the cross section is the coherent sum of two indistinguishable transfer processes. The relative phase between the corresponding transfer amplitudes is obtained from the Pauli principle and depends on the signs of the spectroscopic amplitudes which may, therefore, be determined experimentally.     

Contribution of J-Dependent Potential in Differential Cross-Sections of Two-Nucleon Transfer Reactions

Heavy-ion reactions with two-nucleon transfer are studied within the framework of the distorted wave Born approximation (DWBA) calculations. The bound-states of the transferred particle with the core nucleus forming the projectile or target and residual nuclei are represented by a Yukawa potential. The calculated differential cross-sections are in good agreement with the experimental data. The study exhibits the important contributions of the J-dependent potential in reproducing thelarge-angle oscillatory structures of two-nucleon transfer reactions.     

Direct transfer reactions derived from the green's functions method

Direct transfer reactions are extracted from the general many body theory of nuclear reactions. Especially the case of ground state transitions is considered explicitly for single- and two-nucleon transfer reactions. For this the two- and the three-particle Green's functions respectively are to be used. In deriving theT-matrices of scattering theory plausible assumptions on the energy dependence of the correspondingK-matrices are made. Expressions for direct reactions are obtained which look similar to DWBA. The resultingT-matrices contain microscopic many body expressions for the effective interaction and the optical potentials instead of the phenomenological ones of DWBA.     

Spectroscopy with two-nucleon transfer reactions in deformed nuclei: (I). Form factors

A method for the evaluation of two-nucleon transfer form-factors is devised, which is suitable for the treatment of reactions between deformed nuclei. The nuclear-structure-dependent parts are evaluated in a rotating (intrinsic) frame.     

Effects of the n-n potential core on the spectroscopic sum rules for one-nucleon transfer

Previously derived sum rules are shown to have corrections if the potential contains a hard core. The corrections represent a total loss of single-particle strength which also occurs from the low-energy observable region in the soft-core case. Estimates give a reduction of at least 5 % in the total sum rules, but negligible additional spin-dependent corrections to the partial or spin-dependent sum rules. Important consequences of this lack of spin dependence are pointed out for existing and future sum-rule analyses of spectroscopic data.     

On the extended basis shell model and two-nucleon transfer

The enhancement of two-nucleon transfer reactions predicted by the extended basis shell-model (EBSM) calculations of Feng, Ibarra and Vallieres and other theorists, is shown to be a higher order manifestation of the pairing effects in nuclei. A simple schematic model is introduced which illustrates the constructive interference of the contributions from the highly excited shell-model states included in the EBSM. The model can be used to estimate the effect of ground-state correlations of the closed-shell core. The results indicate that the assumption of an inert core in EBSM calculations introduces negligible error in cases in which the addition of a nucleon pair to a closed shell is treated. However, in the case of two-nucleon removal from a closed shell, including the effects of correlations may significantly enhance the cross section. A suggestion is made for including these effects in EBSM calculations.     

Regge Models and Dispersion Relations for Partial Waves

The asymptotic behaviour of partial wave amplitudes is calculated supposing various Regge models for the total scattering amplitude A(s, t, u). The high energy partial wave behaviour obtained is combined with the validity of partial wave dispersion relations. It is shown that consistency of these assumptions can only be achieved by demanding. 1) a definite asymptotic behaviour of the discontinuity of the left hand cut of partial wave amplitudes. 2) the validity of partial wave sum rules of similar kind as the well-known finite energy sum rules for the total amplitude. All steps of the derivation shall first be demonstrated for elastic scattering of identical scalar particles. Then within the helicity formalism the results are generalized for particles with arbitrary spin and different masses. Finally the question is studied whether the sum rules can be employed to determine unknown CDD-pole parameters in an N/D approach for the I = J = 1/2 state in πN scattering. It is shown that the sum rules of highest order are able to do that.     

Sequential calculations for heavy-ion induced two-nucleon transfer on 14N, 15N and 16O

¹¹B and ¹³C induced two-nucleon transfer data on ¹⁴N, ¹⁵N and ¹⁶O are compared with exact finite-range sequential transfer calculations. The data appear to be consistent with this reaction model and the assumed shell-model structure of the states populated. Single-nucleon transfer data on these targets is also analyzed using the DWBA. Modifications to the exit channel optical potential are required to obtain agreement with shell-model spectroscopic factors.     

Shell-model calculations on Ni and Cu isotopes

Binding energies, excitation energies and spectroscopic factors have been calculated for^57–67Ni and^58–68Cu in an unrestricted (2p_3/2, lf _5/2,2p_1/2) shell-model space. The effective two-body matrix elements are obtained from the modified surface delta interaction (MSDI) and from a least-squares fit to experimental binding and excitation energies (ASDI). The average deviation between about 100 experimental and calculated energies is 0.14MeV for MSDI and 0.08 MeV for ASDI. Excitation energies of high-spin states are given also. Spectroscopic factors have been calculated for all single-nucleon transfer reactions on stable Ni or Cu targets leading to Ni or Cu isotopes. For spectroscopic factors larger than 0.4 the average deviation between theory and experiment is about 30%. The experimentally observed and calculated spectroscopic strengths are compared by using sum rules and are found to be consistent. An extensive compilation has been made of experimental data on energies,J ^π assignments and spectroscopic factors.     

Two-nucleon transfer reactions uphold supersymmetry in atomic nuclei

The spectroscopic strengths of two-nucleon transfer reactions constitute a stringent test for two-nucleon correlations in the nuclear wave functions. A set of closed analytic expressions for ratios of spectroscopic factors is derived in the framework of nuclear supersymmetry. These ratios are parameter independent and provide a direct test of the wave functions. A comparison between the recently measured 198Hg(d-->,alpha)196Au reaction and the predictions from the nuclear quartet supersymmetry lends further support to the validity of supersymmetry in nuclear physics.