Unnatural Parity Transitions Research Articles

Relativistic random-phase-approximation description of M1 excitations with the inclusion of π mesons

Based on the covariant density functional theory, the magnetic dipole ($M1$) resonance is described in the framework of relativistic random-phase approximation with density-dependent meson-nucleon coupling. The isovector-pseudovector interaction channel, represented by the exchange of $\ensuremath{\pi}$ meson, is included in the residual interaction to describe unnatural parity transitions. The strength distributions of $M1$ resonances are studied in doubly magic nuclei $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$, in comparison with their analog Gamow-Teller (GT) excitations. It is found that the $\ensuremath{\pi}$ meson and its zero-range counterterm are responsible for almost all of the energy shift caused by residual interaction, which is similar to the case of GT excitation. However, the strength of the counterterm suggested by the GT study is not suitable to simultaneously reproduce the experimental $M1$ peak energies from $^{48}\mathrm{Ca}$ to $^{208}\mathrm{Pb}$. To improve the descriptions of $M1$, effects caused by adjusting the strength of pionic counterterm and introducing the density dependence of the $\ensuremath{\pi}$ meson channel are explored. Finally, from the analyses of dominant transition configurations of GT and $M1$ resonance, we find that the proper spin-orbit splitting is the key to simultaneously reproduce the $M1$ strength distributions from light to heavy nuclei.

Magnetic dipole excitations based on the relativistic nuclear energy density functional

Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies.

Total Spin Transfer in Continuum for90Zr(p,n) Reaction at 295 MeV

A complete set of polarization transfer observables has been measured for the 90 Zr( p , n ) reaction at T p = 295 MeV and θ lab = 0°. The measurement can yield the total spin transfer Σ(0°) which is independent of nuclear reaction mechanisms such as the effective nucleon–nucleon interaction or distortions. The deduced Σ(0°) values indicate the strong spin-flip characteristics of the continuum up to 50 MeV excitation. A predominance of unnatural-parity transitions in the continuum is also observed from polarization transfer observables.

Analysis of the 11B( 7Li, 7Be) 11Be reaction at 57 MeV in a microscopic approach

The 11B( 7Li, 7Be) 11Be charge exchange reaction has been studied at an incident energy of 57 MeV. Spectra were measured at forward angles, θ cm⩽35°. The good energy resolution (∼50 keV) allowed the identification of transitions both to the 7Be (3/2 −, gs) and 7Be(1/2 −, 429 keV) exit channels and hence the direct measurement of the ratio of the respective cross sections and angular distributions. Besides the bound ground and first excited state of 11Be several low lying excitations just above the neutron threshold are observed. A structure seen at E ∗=9.4 MeV with FWHM ∼7 MeV is compatible with the spin dipole resonance (SDR). The data are analysed in a many-body approach. For the projectile transitions shell model results are used. In order to account properly for the special features of the weakly bound 11Be system the target transitions are described microscopically by Hartree–Fock–Bogoliubov (HFB) and quasi-particle random phase approximation (QRPA) theory. The HFB ground state densities and the QRPA transition densities, respectively, are used in folding calculations for the optical potentials and transition form factors. Spectra and β-decay transitions strengths are reasonably well described. The measured cross section are well reproduced by one-step direct charge exchange distorted wave born approximation (DWBA) calculations. A dominance of unnatural parity transitions is found. This is explained in terms of the spin transfer behaviour of the nucleon–nucleon isovector interaction at low bombarding energy.

Gamow–Teller strength in the continuum and quenching problem

Abstract Differential cross sections at θlab = 0.0°–12.3° and a complete set of polarization transfer observables at θlab = 0.0° are measured for the 90Zr(p, n) reaction at Tp = 295 MeV. A multipole decomposition (MD) technique is applied to the cross sections to extract partial cross sections σL with L=0, 1, 2, and 3 contributions. A significant amount of σL=0 is found in the highly excited continuum region. After subtracting the estimated iso-vector spin-monopole strength from σL=0, the Gamow-Teller (GT) strength B(GT) is deduced to be Sβ− = Σ B(GT) = 28 ± 1.6 ± 5.4. The total spin transfer Σ(0°) which is independent of the nuclear reaction mechanisms such as the effective nucleon-nucleon interaction or distortions is derived from the complete set of polarization transfer observables. It is close to unity up to 50 MeV excitation indicating the strong spin-flip character of the continuum. By using the relation between the polarization transfer observables the fractions of natural-parity and unnatural-parity transitions are also obtained and the dominance of unnatural-parity transitions in the continuum is found. These results are consistent with those derived from the MD analysis. The Sβ− − Sβ+ value is 27.1 and this is 90% of Ikeda's sum rule value of 3(N - Z)=30. Consequently it is concluded that the quenching of the GT strength is small and the quenching mechanism due to the ΔN− admixture seems to play a minor role.

Gamow-Teller strength in the continuum and quenching problem

Differential cross sections at θ lab = 0.0°–12.3° and a complete set of polarization transfer observables at θ lab = 0.0° are measured for the 90Zr( p, n) reaction at T p = 295 MeV. A multipole decomposition (MD) technique is applied to the cross sections to extract partial cross sections σ L with L=0, 1, 2, and 3 contributions. A significant amount of σ L=0 is found in the highly excited continuum region. After subtracting the estimated iso-vector spin-monopole strength from σ L=0 , the Gamow-Teller (GT) strength B(GT) is deduced to be S β − = Σ B(GT) = 28 ± 1.6 ± 5.4. The total spin transfer Σ(0°) which is independent of the nuclear reaction mechanisms such as the effective nucleon-nucleon interaction or distortions is derived from the complete set of polarization transfer observables. It is close to unity up to 50 MeV excitation indicating the strong spin-flip character of the continuum. By using the relation between the polarization transfer observables the fractions of natural-parity and unnatural-parity transitions are also obtained and the dominance of unnatural-parity transitions in the continuum is found. These results are consistent with those derived from the MD analysis. The S β − − S β + value is 27.1 and this is 90% of Ikeda's sum rule value of 3( N - Z)=30. Consequently it is concluded that the quenching of the GT strength is small and the quenching mechanism due to the ΔN − admixture seems to play a minor role.

Configuration mixing in 56Co and 46Sc using (d

Two-nucleon spectroscopic amplitudes are investigated using cross-section measurements and tensor analyzing powers for the $^{58}\mathrm{Ni}$(d\ensuremath{\rightarrow},\ensuremath{\alpha}${)}^{56}$Co and $^{48}\mathrm{Ti}$(d\ensuremath{\rightarrow},\ensuremath{\alpha}${)}^{46}$Sc reactions. Angular distributions of cross sections, and analyzing powers ${\mathit{A}}_{\mathit{y}}$, ${\mathit{A}}_{\mathit{x}\mathit{x}}$, and ${\mathit{A}}_{\mathit{y}\mathit{y}}$, were measured in steps of 5\ifmmode^\circ\else\textdegree\fi{} from 10\ifmmode^\circ\else\textdegree\fi{} to 65\ifmmode^\circ\else\textdegree\fi{} at a bombarding energy of 22 MeV. Data were analyzed using full finite-range DWBA calculations including a realistic \ensuremath{\alpha}-particle wave function. The L-mixing ratios for several strong unnatural-parity transitions have been determined from comparison of calculations with analyzing power data. These ratios are compared to predictions of shell-model calculations to deduce predominant two-nucleon configurations.

Density dependent interaction applied to low-multipole (p,p') and (p,n) transitions in light nuclei.

The density-dependent interaction based on the Bonn-J\"ulich G-matrix NN interaction was used in a distorted-wave Born approximation analysis of (p,p') and (p,n) data for p-shell nuclei at ${\mathit{E}}_{\mathit{p}}$=35 MeV. Calculations with this interaction fit the data as well as the commonly used density-independent interaction M3Y and gave significant improvement for analyzing powers of unnatural-parity transitions. Most of the improvement was found to be due to the tensor part of the interaction.

36,38Ar(d-bar, alpha )34,36Cl reactions induced by tensor polarized deuterons.

Exact finite-range distorted-wave Born approximation analyses of cross section and vector and tensor analyzing power angular distributions for some /sup 36,38/Ar(d-arrow-right,..cap alpha..) transitions induced by 16 MeV polarized deuterons have been performed using full s-italicd-italic-shell model wave functions and including a D-italic-state amplitude for the ..cap alpha.. particle. The L-italic-mixing ratios R-italic for several unnatural parity transitions have been determined from comparisons of the calculations with the tensor analyzing power data. Shell-model calculations are found to be in agreement with the experimentally obtained phases of R-italic, while the predicted magnitudes agree well in some cases.

The role of sequential transfer in unnatural-parity transitions in the 208Pb(p, t) 206Pb reaction

Angular distributions have been obtained for several unnatural-parity transitions in the 208Pb(p, t) 206Pb reaction at E p = 20.0 and 50.5 MeV. It is found that the sequential (p, d) (d, t) process provides an adequate description of these transitions at both energies.

Nuclear information from the proton spin observables in the (p, p′) reactions at intermediate energies

A set of proton spin observables ${D}_{\ensuremath{\xi}}$, $\ensuremath{\xi}=0, x, y, \mathrm{and} z$, is described which provides selective information on the tensor components of the collision matrix describing the ($p, {p}^{\ensuremath{'}}$) reaction. These ${D}_{\ensuremath{\xi}}$ are related linearly to the experimentally determined components of the depolarization tensor. Simple relations are derived between the ${D}_{\ensuremath{\xi}}$ and both the spin components of the nucleon-nucleon amplitudes and the nuclear multipole form factors. For unnatural parity transitions the observable ${D}_{x}$ is related to the axial longitudinal form factor which does not enter in the ($e, {e}^{\ensuremath{'}}$) transition amplitudes for the one photon exchange mechanism.NUCLEAR REACTIONS New polarization parameters in ($p, {p}^{\ensuremath{'}}$) reactions.

An Approach for the DWBA Calculation of the Two-Nucleon Transfer (p, t) Reaction

A new approach of the DWBA calculation for the (p, l) reaction is investigated. The DWBA term is calculated as the two-step non-orthogonality term for Ca(p, t)46Ca(O+, g.s.) reaction at E p =20 MeV and 40 MeV. This, together with the two-step (P-d-l) amplitude calculated by the quasi-particle method, gives the full reaction amplitude in the present scheme. Further, the coherence property of the two-step amplitude is discussed. 6 ),7) who insist that the absolute cross section and the angular distribution of the (p, t) reaction (or ( t, p) reaction) are well described by the one-step DWBA. They analyzed the DWBA term for some cases with a wave function for the triton, and pointed out the importance of improving the form factor for the transferred two neutrons and of using the wave function for the triton. Nowadays, it is still difficult to get a triton wave function, even by means of solving the Faddeev equations or using variational approaches with potentials. It is well known that the wave functions calculated by such methods do not fully reproduce the binding energy and the charge form factor, etc. Thus, the use of the realistic triton wave function for the DWBA calculation in the (p, t) reactions is, strictly speaking, not always appropriate, and, possibly the conclusion obtained by means of such a treatment will be altered in future, especially in the analyses of the polarization phenomena and the unnatural parity transitions. In this paper, we propose a method of calculating the DWBA term accurately and discuss the reaction mechanism. The idea of our approach is to use the mechanism of the cancellation between the non-orthogonality term and the DWBA term. 9 ) In the DWBA calculation of the two-nucleon transfer reaction, we generally encounter the difficulty that the form factor cannot be constructed

Unnatural parity transitions in (p,t) reactions using realistic triton wavefunctions

The reaction 208Pb(p,t) 206Pb leading to the unnatural parity 3 + state of 206Pb is analyzed in the framework of finite range DWBA formalism. The main aspect of the present analysis is the use of a realistic triton wavefunction with S, S′ and D state components which permit this transition in DWBA. Excellent agreement between theoretical prediction and experiment is obtained casting serious doubt on the treatment of this reaction as a sequential transfer process.

Selection rules in DWBA theory of (p, t) reactions

Angular momentum selection rules for (p, t) reactions within the framework of DWBA formalism are given for the particular case where the triton wavefunction is classified according to its orbital permutation symmetry. The selection rules demonstrate that certain previous calculations of unnatural parity transitions should exactly vanish, and suggest the important result that “weak” unnatural parity transitions can occur as direct one step reactions via the mixed symmetry S and D state components of the triton wavefunction.

Monte Carlo calculations of two-neutron transfer cross sections

Differential cross sections for (t, p) and (p, t) reactions have been calculated in finite-range distorted-wave Born approximation, with the Monte Carlo method used to evaluate the six-dimensional integrals. The use of the Monte Carlo method makes it possible to treat cases of non-zero angular momentum transfer. Angular distributions and relative cross sections are in good agreement with those given by the zero-range approximation. The cross sections of unnatural-parity transitions, as calculated by our one-step finite-range DWBA, are several orders of magnitude smaller than experimental data, suggesting the importance in these reactions of two-step processes.