Isovector M1 Transitions Research Articles

Nuclear magnetic transitions in the relativistic energy density functional approach

Recently a novel theory framework has been established for description of magnetic dipole (M1) transitions in finite nuclei, based on relativistic nuclear energy density functional with point coupling interactions. The properties of M1 transitions have been studied, including the sum rules, spin, orbital, isoscalar and isovector M1 transition strengths in magic and open shell nuclei. It is shown that pairing correlations and spinorbit interaction plays an important role in the description of M1 transition strength distributions. The analysis of the evolution of M1 transition properties in the isotope chain100-140Sn shows the interplay between single and double-peak structures, determined by the evolution of single-particle states, their occupations governed by the pairing correlations, and two-quasiparticle transitions involved. Comparison of the calculated B(M1) transition strength with recent data from inelastic proton scattering on112-124Sn, shows that quenching of thegfactorsgeff/gfree=0.80-0.93 is required to reproduce the experimental data. Further experimental investigations are needed to determine accurately the quenching factor.

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.

Decay strength distributions inC12(C12,γ) radiative capture

The heavy-ion radiative capture reaction, {sup 12}C({sup 12}C,{gamma}), has been investigated at energies both on- and off-resonance, with a particular focus on known resonances at E{sub c.m.}=6.0, 6.8, 7.5, and 8.0 MeV. Gamma rays detected in a BGO scintillator array were recorded in coincidence with {sup 24}Mg residues at the focal plane of the DRAGON recoil separator at TRIUMF. In this manner, the relative strength of all decay pathways through excited states up to the particle threshold could be examined for the first time. Isovector M1 transitions are found to be a important component of the radiative capture from the E{sub c.m.}=6.0 and 6.8 MeV resonances. Comparison with Monte Carlo simulations suggests that these resonances may have either J=0 or 2, with a preference for J=2. The higher energy resonances at E{sub c.m.}=7.5 and 8.0 MeV have a rather different decay pattern. The former is a clear candidate for a J=4 resonance, whereas the latter has a dominant J=4 character superposed on a J=2 resonant component underneath. The relationship between these resonances and the well-known quasimolecular resonances as well as resonances in breakup and electrofission of {sup 24}Mg into two {sup 12}C nuclei are discussed.

Proton-neutron symmetry in N=Z nuclei

The analysis of new experimental data, rotor-plus-quasideuteron and shell model calculations for the odd-odd N=Z nuclei 46V and 50Mn is presented. Low-lying low-spin states exhibiting collective properties appropriate for the K=0, K=3, and K=5 bands are identified. The strong isovector M1 transitions of quasideuteron origin in 46V and 50Mn are shown to be important indicators for collective features and perfectly fit into the systematics of M1 transitions in odd-odd N=Z nuclei.

Toward isovector M1 transitions in odd-odd N = Z nuclei

IsovectorM1 transitions between low-lying T=1 and T=0 states in odd-odd N = Z nuclei are discussed. The data on low-spin states in the odd-odd nuclei 46V and 50Mn investigated with the 46Ti(p, nγ)46V and 50Cr(p, nγ)50Mn fusion evaporation reactions at the FN-TANDEM accelerator in Cologne are reported. A simple explanation of the enhancement of the M1 transitions is given in terms of quasideuteron configurations. The fragmentation of the strong M1 transitions is shown to be due to the coupling of the two-particle configurations to the rotating core.

Quasideuteron configurations in 46V and 58Cu

The data on low spin states in the odd-odd nuclei 46V and 58Cu investigated with the 46Ti(p,ngamma)46V, 32S(16O,pn)46V and 58Ni(p,ngamma)58Cu reactions at the FN-TANDEM accelerator in Cologne are reported. The states containing large quasideuteron components are identified from the strong isovector M1 transitions, from shell model calculations and from experimental data for low-lying states.

Approaching rotational collectivity in odd-odd NZ nuclei in pf-shell

The analysis of shell model wave functions and new experimental data for odd-odd NZ nuclei 46V and 50Mn is presented in terms of collective rotor-plus-quasideuteron model. The low-lying low-spin states exhibiting collective properties appropriate for the K=0, K=3, and K=5 bands are identified. The strong isovector M1 transitions of quasideuteron origin in 46V and 50Mn are shown to be important indicators of collective features and to give more complete information on the structure of the intrinsic states than E2 matrix elements.

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in 28Si are considered, and the lifetimes of 1+ states in 28Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1+ state at 2.201 MeV in 28Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a 28Si nucleus among the 1+ states of the final nucleus 28Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.

Low spin structure of odd-odd N=Z nuclei

Isovector M1 transitions between low-lying T=1 and T=0 states in odd-odd N=Z nuclei are discussed. Simple analytical expressions for M1 transition strengths are given in single-j-shell approximation. The large B(M1) values for the j = l + 1 2 case are attributed to quasi-deuteron configurations. The B(M1) values for the j = l − 1 2 case are found to be small due to a cancellation of spin and orbital parts of the M1 matrix element. The experimental data on low spin states in the odd-odd nuclei 54Co and 46V investigated with the 54Fe(p, nγ) 54Co and 46Ti(p, nγ) 46V fusion reactions at the EN- tandem accelerator in Cologne are reported. The J π = 0 1 +, 2 1 +, 4 1 + T=1 and J π = 1 1 +, 3 1 +, T=0 states in 54Co are identified as predominantly πf 7 2 −1 × νf 7 2 −1 quasi-deuteron states.

Quasideuteron configurations in odd-oddN=Znuclei

The isovector M1 transitions between low-lying T=1 and T=0 states in odd-odd N=Z nuclei are analyzed. Simple analytical expressions for M1 transition strengths are derived within a single-j-shell approximation for both j=l+1/2 and j=l-1/2 cases. The large B(M1) values for the j=l+1/2 case are attributed to quasi-deuteron configurations. The B(M1) values for the j=l-1/2 case are found to be small due to partly cancellation of spin and orbital parts of the M1 matrix element.

Microscopic SUπ(3)⊗SUν(3) interpretation of a two triaxial rotor model

A description of the relative motion of neutrons and protons in strongly deformed even-even nuclei is reduced to that of two coupled triaxial rotors, one representing the neutrons and the other the protons, by using generating function methods. The two rotor theory is interpreted as a generalization of the Elliott SU(3) model with a neutron–proton direct product SUν(3)×SUπ(3) substructure. The second order Casimir operator for this system is constructed and some of its eigenfunctions are found in explicit form in the Fock–Bargmann space representation. Analytical results for isovector M1 transitions probabilities are obtained and the results compared with experimental data and pseudo-SU(3) calculations. Graphs picturing the relative orientation of neutron-proton rotors in Ne22 are presented.

Isovector M1 transitions in 28Si and the role of meson exchange currents.

At the newly installed 180\ifmmode^\circ\else\textdegree\fi{} Darmstadt electron scattering facility we have measured the isovector M1 transition strengths in $^{28}\mathrm{Si}$ in the excitation energy range from 10 to 18 MeV. Overall agreement with a shell-model calculation using the unified sd-shell interaction and effective g factors is obtained. Comparison with Gamow-Teller strength deduced from (p,n) data reveals the presence of meson exchange current contributions of the order of 25% to the summed M1 transition strength. \textcopyright{} 1996 The American Physical Society.

Shell-model calculations of isovector electromagnetic transitions and Gamow-Teller beta decays in the N

Isovector E2 and M1 transitions from isobaric analog states of the N=29 isotones to low-lying states in the N=28 isotones are discussed by making use of the shell model. The ${f}_{7/2}^{n\mathrm{\ensuremath{-}}1}$j and the ${f}_{7/2}^{n}$+${f}_{7/2}^{n\mathrm{\ensuremath{-}}1}$j configurations are assumed for the N=29 and N=28 isotones, respectively, where j denotes one of the ${p}_{3/2}$, ${p}_{1/2}$, and ${f}_{5/2}$ orbits. First, the model space is restricted to j=${p}_{3/2}$ only, and it is extended to include all the ${p}_{3/2}$, ${p}_{1/2}$, and ${f}_{5/2}$ orbits, in order to study stepwise the role of the various wave function components. For the isovector E2 transitions, it is confirmed that the major components of the wave functions play a decisive role for the allowed transitions in the single-particle shell model and the use of the good isospin wave functions is indispensable for the forbidden ones. For the isovector M1 transitions, it is shown that the spin-nonflip ${f}_{7/2}$\ensuremath{\rightarrow}${f}_{7/2}$ transition, which is introduced by the neutron-excited components in the wave functions of the N=28 isotones, plays a very significant role: It gives rise to the important cancellation which is responsible for the strong suppression of the M1 transition strength in comparison with the simple shell-model prediction, and it becomes the leading term in the l- and j-forbidden M1 transitions. Similar discussion holds for the Gamow-Teller beta decays between the levels of the N=28 and N=29 nuclei.

Shell model and IBM descriptions of mixed symmetry or isovector M1 transitions in the titanium isotopes

M1 strengths are calculated in the shell model for the titanium isotopes and the results are interpreted in the language of the interacting boson model. The influence of the g boson is discussed.

The ß-decay of 48Cr and low energy collective M1 transitions

A measured half-life for the ß-decay of 48Cr is used to provide information on the spin contribution to a collective isovector M1 transition.

SU(4) breaking ground-state correlations and quenching of Gamow-Teller and isovector M1 transitions

It is shown that SU(4) breaking ground-state correlations in 16O or 40Ca can provide a quenching of about 10–15% for Gamow-Teller and isovector M1 transition amplitudes in neighbouring nuclei with A = 15, 17, 39 and 41.

High-resolution (e, e') study of isovector M1 and M2 transitions in the oxygen isotopes: (III). 18O

The excitation energy region in 18O from about E x = 11–27 MeV has been studied with low-momentum transfer, but high-resolution inelastic electron scattering. Two sharp lines are prominent in the spectra, corresponding to the excitation of T = 2 levels at 16.399 ± 0.005 MeV and 18.871 ± 0.005 MeV of J π = 2 − and 1 +, respectively. In contradiction to theoretical predictions no more strong M2 transitions could be found. Broad peaks were observed at 18.5, 19.7, 20.2, 22.5 and 23.8 MeV, the latter two are due to the giant dipole resonance as known from photonuclear reactions. The spectra show in addition considerable fine structure and the application of a cross correlation function technique for its analysis resulted in the location of twelve more low multipolarity weak transitions in the excitation energy range between 16 and 19 MeV. Tentative J π assignments are given for these levels. The spectra of isospin T = 2 states of A = 18 nuclei are discussed in view of the existing experimental and theoretical work. Finally, the pattern of the isovector M1 and M2 strength distributions of all the three oxygen isotopes 16,17,18O is discussed.

High-resolution (e, e') study of isovector M1 and M2 transitions in the oxygen isotopes: (II). 17O

In a high-resolution electron scattering experiment, six isospin T = 3 2 levels in the excitation energy region of 11–15.3 MeV were populated in 17O. Five transitions at E x = 11.08, 12.47, 12.99, 14.23 and 14.75 MeV are predominantly of M2 nature with transition strengths B(M2, k)↑ = 6.1 ± 1.9, 6 ± 3, 6 ± 3, 46 ± 7 and 27 ± 9 μ N 2 · fm 2, respectively. The transition to the 15.10 MeV level is mainly M1 with B(M1, k)↑ = 0.14 ± 0.04 μ N 2. For this level, a tentative spin-parity assignment of J π = 3 2 + is possible. Also, a spin assignment of J π = 9 2 − is preferred for the 14.75 MeV level. The comparison of the transition strength to the level at 11.08 MeV with the prediction from the analogous unique first-forbidden β − decay of the 17N ground state indicates that it may be important to include p 3 2 -hole configurations in the ground-state wave function of 17O. A comparison made with the corresponding E1 transitions in 17F, by estimating the possible longitudinal component for the 14.23 MeV transition and assuming that the 12.99 MeV transition is pure E1, shows that mirror asymmetries in the mass 17 pair may be of non-zero magnitudes.

High-resolution (e, e') study of isovector M1 and M2 transitions in the oxygen isotopes: (I). 16O

The M1 and M2 transition strength distribution for 16O in the excitation energy range from 16 to 20 MeV has been measured in a high-resolution electron scattering experiment. The M1 strength is concentrated in three sharp states at E x = 16.22, 17.14 and 18.79 MeV (± 0.01 MeV) with B(M1, k)↑ = 0.20 ± 0.02, 0.32 ± 0.03 and 0.13 ± 0.03 μ N 2, respectively. An additional strength of 0.35 ± 0.09 μ N 2, distributed over eight weakly excited states with excitation energies E x = 17.4 to 18.0 MeV, brings the total measured M1 strength to B(M1, k)↑ = 1.0 ± 0.1 μ N 2. The experimental M2 strength is distributed over states at E x = 16.82, 17.78, 18.50 and 19.0 MeV (± 0.01 MeV) with B(M2, k)↑ = 19 ± 2, 13 ± 2, 59 ± 7 and 341 ± 51 μ N 2 · fm 2, respectively. Electric transitions were also measured to states at E x = 16.45 MeV (2 +, E2), 17.30 MeV (1 +, E1) and 18.20 MeV (2 +, E2). Calculations were performed using the modified surface delta interaction in a 2p-2h shell model for the M1 transitions and the random phase approximation for the M2 transitions. The results show the sensitivity of the M1 strength as a measure of ground-state correlations and compare well with results from the 15N( p , γ) reaction.

Importance of the orbital magnetization for isovectorM1transitions of nuclei in thesdshell

The spin and orbital-current contributions to isovector M1 transitions in light nuclei are studied using shell model wave functions. An impressive effect of the orbital magnetization is predicted for /sup 20/Ne and demonstrated by comparing the M1-strength distributions for inelastic electron scattering with the distribution for radiative pion capture and (p,n) reactions.