Monopole Transitions Research Articles

Study of the Alpha-particle Monopole Transition form Factor

Study of the Alpha-particle Monopole Transition form Factor

The LSU-Argonne conversion electron spectrometer: A new detector for the X-Array and SATURN decay station

A new conversion electron detector has been commissioned at the ATLAS/ CARIBU facility at Argonne National Laboratory. The LSU-Argonne Conversion Electron Spectrometer (LACES) is a LN2-cooled Si(Li) detector system designed to be incorporated into a decay station that comprises the dedicated HPGe clover array with a box geometry (X-Array) and the Scintillator and Tape Using Radioactive Nuclei (SATURN) device. This integration enables simultaneous measurements of conversion electrons and gamma-rays in decay experiments, yielding novel information on transition multipolarities, electric monopole transitions, and isomeric states that decay mostly via conversion electrons. A measurement of the energy resolution of LACES yielded 2.3-keV FWHM at 975 keV for electrons and 1.3-keV FWHM at 75 keV for X-rays. A detailed study of the absolute detection efficiency (at 5 mm from the source) was performed, where this quantity was determined experimentally in the range of electron transition energies between 25.5 keV and 1047.8 keV and subsequently simulated using the GEANT4 code. Measurement and simulations are found to be in excellent agreement. A precise characterization, for this type of detector system, of the absolute detection efficiency for such a wide energy range is reported for the first time.

AbInitio Calculation of the Alpha-Particle Monopole Transition Form Factor.

We present a parameter-free abinitio calculation of the α-particle monopole transition form factor in the framework of nuclear lattice effective field theory. We use a minimal nuclear interaction that was previously used to reproduce the ground state properties of light nuclei, medium-mass nuclei, and neutron matter simultaneously with no more than a few percent error in the energies and charge radii. The results for the monopole transition form factor are in good agreement with recent precision data from Mainz.

Investigations of electric monopole transitions in medium-mass to heavy nuclei: Beyond mean field calculations with the Gogny force

Investigations of electric monopole transitions in medium-mass to heavy nuclei: Beyond mean field calculations with the Gogny force

Observation of the Exotic 0_{2}^{+} Cluster State in ^{8}He.

We report here the first observation of the 0_{2}^{+} state of ^{8}He, which has been predicted to feature the condensatelike α+^{2}n+^{2}n cluster structure. We show that this state is characterized by a spin parity of 0^{+}, a large isoscalar monopole transition strength, and the emission of a strongly correlated neutron pair, in line with theoretical predictions. Our finding is further supported by the state-of-the-art microscopic α+4n model calculations. The present results may lead to new insights into clustering in neutron-rich nuclear systems and the pair correlation and condensation in quantum many-body systems under strong interactions.

Description of the Proton-Decaying 0_{2}^{+} Resonance of the α Particle.

The recent precise experimental determination of the monopole transition form factor from the ground state of ^{4}He to its 0_{2}^{+} resonance via electron scattering has reinvigorated discussions about the nature of this first excited state of the α particle. The 0_{2}^{+} state has been traditionally interpreted in the literature as the isoscalar monopole resonance (breathing mode) or, alternatively, as a particle-hole shell-model excitation. To better understand the nature of this state, which lies only ∼410 keV above the proton emission threshold, we employ the coupled-channel representation of the no-core Gamow shell model. By considering the [^{3}H+p], [^{3}He+n], and [^{2}H+^{2}H] reaction channels, we explain the excitation energy and monopole form factor of the 0_{2}^{+} state. We argue that the continuum coupling strongly impacts the nature of this state, which carries characteristics of the proton decay threshold.

Emergence of triaxiality in 74Se from electric monopole transition strengths

The structure of 74Se at low energy was investigated via spectroscopy of internal conversion electrons at the INFN Legnaro National Laboratories (LNL). A set of internal K-conversion coefficients and monopole transition strengths was measured. A large ρ2(E0;22+→21+)⋅103=210(130) value was deduced. This result, in addition to a low upper limit for the 03+→02+ electron transition, casts in doubt a simple interpretation of the 74Se low-lying structure, in particular the recently proposed spherical, vibrational character. New microscopic beyond-mean-field calculations generally agree with the experimental results and are capable of producing a large ρ2(E0;22+→21+) value, even if still a factor ≈7 smaller than the experiment. Triaxiality and a complex shape-coexistence and mixing scenario seem responsible for this unexpected experimental result.

Derivation of transition density from the observed 4He(e, e′)4He(02+) form factor raising the α-particle monopole puzzle

Abstract Recently, the monopole transition form factor of the electron-scattering excitation of the $0^+_2$ state (Ex = 20.21 MeV) of the 4He nucleus was observed over a broad momentum transfer range ($0.5 \le q^2 \le 5.0 \, {\rm fm}^{-2}$) with dramatically improved precision compared with older sets of data; modern nuclear forces, including those derived from the chiral effective field theory, failed to reproduce the form factor, which is called the α-particle monopole puzzle. To resolve this puzzle by improving the study of the spatial structure of the $0^+_2$ state, we derive in this letter a possible $0^+_1\!\rightarrow \! 0^+_2$ transition density ρtr(r) for r ≳ 1 fm from the observed form factor. The shape of the transition density is significantly different from that obtained theoretically in the literature.

Measurement of the α-Particle Monopole Transition Form Factor Challenges Theory: A Low-Energy Puzzle for Nuclear Forces?

We perform a systematic study of the α-particle excitation from its ground state 0_{1}^{+} to the 0_{2}^{+} resonance. The so-called monopole transition form factor is investigated via an electron scattering experiment in a broad Q^{2} range (from 0.5 to 5.0 fm^{-2}). The precision of the new data dramatically supersedes that of older sets of data, each covering only a portion of the Q^{2} range. The new data allow the determination of two coefficients in a low-momentum expansion, leading to a new puzzle. By confronting experiment to state-of-the-art theoretical calculations, we observe that modern nuclear forces, including those derived within chiral effective field theory that are well tested on a variety of observables, fail to reproduce the excitation of the α particle.

Evidence for prolate-oblate shape coexistence in the odd- ABr383573 nucleus

The excited states in $^{73}\mathrm{Br}$ nucleus have been investigated through the fusion evaporation reaction $^{50}\mathrm{Cr}(^{28}\mathrm{Si}$, $\ensuremath{\alpha}p)^{73}\mathrm{Br}$ at a beam energy of 90 MeV using the Indian National Gamma Array. The $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence technique has been used to add eight new $\ensuremath{\gamma}$-ray transitions in the level scheme. The mixing ratio of $\mathrm{\ensuremath{\Delta}}I=0$ (mixed with $E2$ and $M1$) transitions have been determined using angular distribution and ${R}_{\mathrm{DCO}}$-polarization measurement. The half-life of the ${9/2}^{+}$ isomeric state has been measured to be ${\ensuremath{\tau}}_{1/2}=52(2)$ ns from the variation in the intensity of delayed $\ensuremath{\gamma}$-ray transition as a function of coincidence time window. The two state mixing model calculations were performed to obtain the mixing amplitude, and mixing interaction of two different configurations of $^{73}\mathrm{Br}$. The calculated mixing amplitudes along with the deformations of two different configurations provide the monopole transition strength ${\ensuremath{\rho}}^{2}(E0)$ for Se, Br, and Kr isotopes in a semiempirical approach. These results support a prolate-oblate shape coexistence in the odd-$A\phantom{\rule{4pt}{0ex}}^{73}\mathrm{Br}$ nucleus. The observed structural properties have been discussed in terms of projected shell model calculations.

Reassigning the shapes of the 0+ states in the 186Pb nucleus

Across the physics disciplines, the 186Pb nucleus is the only known system, where the two first excited states, together with the ground state, form a triplet of zero-spin states assigned with prolate, oblate and spherical shapes. Here we report on a precision measurement where the properties of collective transitions in 186Pb were determined in a simultaneous in-beam γ-ray and electron spectroscopy experiment employing the recoil-decay tagging technique. The feeding of the {0}_{2}^{+} state and the interband {2}_{2}^{+}to {2}_{1}^{+} transition have been observed. We also present direct measurement of the energies of the electric monopole transitions from the excited 0+ states to the 0+ ground state. In contrast to the earlier understanding, the obtained reduced transition probability B(E2;{2}_{1}^{+}to {0}_{2}^{+}) value of 190(80) W.u., the transitional quadrupole moment | {Q}_{t}({2}_{1}^{+}to {0}_{2}^{+})| =7.7(33) eb and intensity balance arguments provide evidence to reassign the {0}_{2}^{+} and {0}_{3}^{+} states with predominantly prolate and oblate shape, respectively. Our work demonstrates a step-up in experimental sensitivity and paves the way for systematic studies of electric monopole transitions in this region. These electric monopole transitions probe the nuclear volume in a unique manner and provide unexploited input for development of the next-generation energy density functional models.

Signatures of shape phase transitions in krypton isotopes based on relativistic energy density functionals

Spectroscopic properties that characterize the shape phase transitions in krypton isotopes with the mass $A\approx80$ region are investigated within the framework of the nuclear density functional theory. Triaxial quadrupole constrained self-consistent mean-field calculations that employ relativistic energy density functionals and a pairing interaction are carried out for the even-even nuclei $^{76-86}$Kr. The spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with the ingredients, i.e., the deformation-dependent moments of inertia and mass parameters, and the collective potential, determined by using the SCMF solutions as microscopic inputs. Systematic behaviors of the SCMF potential energy surfaces, the corresponding low-energy spectra, electric quadrupole and monopole transition probabilities, and the fluctuations in the triaxial quadrupole deformations indicate evolution of the underlying nuclear structure as functions of the neutron number, that is characterized by a considerable degree of shape mixing. A special attention is paid to the transitional nucleus $^{82}$Kr, which has been recently identified experimentally as an empirical realization of the E(5) critical-point symmetry.

Electric Monopole Transition from the Superdeformed Band in ^{40}Ca.

The electric monopole (E0) transition strength ρ^{2} for the transition connecting the third 0^{+} level, a "superdeformed" band head, to the "spherical" 0^{+} ground state in doubly magic ^{40}Ca is determined via e^{+}e^{-} pair-conversion spectroscopy. The measured value ρ^{2}(E0;0_{3}^{+}→0_{1}^{+})=2.3(5)×10^{-3} is the smallest ρ^{2}(E0;0^{+}→0^{+}) found in A<50 nuclei. In contrast, the E0 transition strength to the ground state observed from the second 0^{+} state, a band head of "normal" deformation, is an order of magnitude larger ρ^{2}(E0;0_{2}^{+}→0_{1}^{+})=25.9(16)×10^{-3}, which shows significant mixing between these two states. Large-scale shell-model (LSSM) calculations are performed to understand the microscopic structure of the excited states and the configuration mixing between them; experimental ρ^{2} values in ^{40}Ca and neighboring isotopes are well reproduced by the LSSM calculations. The unusually small ρ^{2}(E0;0_{3}^{+}→0_{1}^{+}) value is due to destructive interference in the mixing of shape-coexisting structures, which are based on several different multiparticle-multihole excitations. This observation goes beyond the usual treatment of E0 strengths, where two-state shape mixing cannot result in destructive interference.

Electric monopole transitions and structure of low-spin states in Pd106

Structures in the $^{106}\mathrm{Pd}$ nucleus have been studied in the $\mathrm{EC}/{\ensuremath{\beta}}^{+}$ decay of $^{106}\mathrm{Ag}$ at the INFN Legnaro National Laboratories using the Spes Low-energy Internal Conversion Electron Spectrometer (SLICES). The K-conversion coefficients and the electric monopole transition strengths, between low-lying ${2}^{+}$ and ${0}^{+}$ states, have been studied. These experimental data combined with the results from conversion electron measurement on $^{104}\mathrm{Pd}$ previously performed by the Florence spectroscopy group were compared with the theoretical values calculated in the framework of the interacting proton-neutron boson model. Good agreement between experimental and theoretical values is found when interpreting the ${0}_{3}^{+}$ level as an intruder state.

Erosion of N = 28 shell closure: Shape coexistence and monopole transition

Abstract In neutron-rich nuclei neighboring 42Si, the quenching of the N = 28 shell gap occurs and is expected to induce shape coexistence in their excitation spectra. We have applied the theoretical framework of antisymmetrized molecular dynamics with the Gogny D1S density functional to describe the shape coexistence in the N = 28 isotones 40Mg, 42Si, and 44S. We show that different nuclear shapes coexist in these nuclei: Rigid shapes with different deformations coexist in 40Mg and 42Si, while 44S exhibits large-amplitude collective motion and does not have any particular shape. These characteristics are reflected well in the monopole transition strengths that can be utilized as a probe for the shape coexistence.

Correspondence between isoscalar monopole strengths and $\alpha$ inelastic cross sections on 24Mg

Abstract The correspondence between the isoscalar monopole (IS0) transition strengths and $\alpha$ inelastic cross sections, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence, is investigated for $^{24}$Mg($\alpha,\alpha'$) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for $^{24}$Mg obtained with antisymmetrized molecular dynamics to the ($\alpha,\alpha'$) cross sections. We aim at clarifying how the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon–nucleon effective interaction in the scattering process, and the coupled-channel effect. It is found that these effects are significant and the explanation of the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the $0^+$ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%–30%, while it is seriously compromised at 130 MeV, mainly by the strong nuclear distortion. It is also found that when a $0^+$ state that has a different structure from a simple $\alpha$ cluster state is considered, the $B({\rm IS0})$–$(\alpha,\alpha')$ correspondence becomes less valid. For a quantitative discussion on the $\alpha$ clustering in $0^+$ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.

Search for $\alpha$ condensed states in $^{13}$C using $\alpha$ inelastic scattering

AbstractWe searched for the $\alpha$ condensed state in $^{13}$C by measuring the $\alpha$ inelastic scattering at $E_\alpha = 388$ MeV at forward angles including 0$^\circ$. We performed a distorted-wave Born approximation calculation with the single-folding potential and multipole decomposition analysis to determine the isoscalar transition strengths in $^{13}$C. We found a bump structure around $E_x = 12.5$ MeV due to the isoscalar monopole ($IS0$) transition. A peak-fit analysis suggested that this bump consisted of several $1/2^-$ states. We propose that this bump is due to the mirror state of the 13.5 MeV state in $^{13}$N, which dominantly decays to the $\alpha$ condensed state in $^{12}$C. It was speculated that the $1/2^-$ states around $E_x = 12.5$ MeV were candidates for the $\alpha$ condensed state, but the $3\alpha + n$ orthogonality condition model suggests that the $\alpha$ condensed state is unlikely to emerge as the negative parity states. We also found two $1/2^+$ or $3/2^+$ states at $E_x = 14.5$ and 16.1 MeV excited with the isoscalar dipole ($IS1$) strengths. We suggest that the 16.1 MeV state is a possible candidate for the $\alpha$ condensed state predicted by the cluster model calculations on the basis of the good correspondence between the experimental and calculated level structures. However, the theoretical $IS1$ transition strength for this state is significantly smaller than the measured value. Further experimental information is strongly desired to establish the $\alpha$ condensed state in $^{13}$C.

Extended analytical solutions of the Bohr Hamiltonian with the sextic oscillator

Low-lying collective quadrupole states in even–even nuclei are studied for the particular case of a γ-unstable potential within the Bohr Hamiltonian. In particular, the quasi-exactly solvable β-sextic potential is extended to cover the most relevant part of the low-lying spectra in nuclei. In previous papers (2004 Phys. Rev. C 69 014304, 2010 Phys Rev. C 81 044304), the same situation was solved for β-wavefunctions with up to one node (M = 0, 1), which are relevant for the first few low-lying states. Here, the model space is enlarged by including β-wavefunctions also with two nodes (M = 2), which generate many more states, in order to make it useful for actual fittings and more detailed checking of shape phase transitions between spherical and γ-unstable β-deformed shapes in nuclei. In addition to the energy eigenvalues and wavefunctions, closed analytical formulas are obtained for electric quadrupole and monopole transition probabilities too. The model is applied to the chains of even Ru and Pd isotopes to illustrate the transition between the spherical and deformed γ-unstable phases. These applications indicate that the optional extension of the model with a phenomenologic rotational term L ⋅ L is consistent with the experimental data.

Transitions probabilities B(E2), B(M1) and B(E0) in 130Ba isotope

Nuclear structure for even-even 130Ba isotope have been investigated. They examined carefully with IBM1 and IBM2. Low lying energy levels for even even positive parity states, reduced electric quadruple transitions probabilities B(E2), branching ratios, reduced magnetic dipole transitions probability B(M1), reduced electric monopole transitions probability B(E0), and mixing ratio X(E0/E2) have been studied.In the framework of IBM1 noted the competition between the two parameters (a 0 and a 2) in 130Ba isotope was the increases of a0 associated with decreases of a2 which mean that the γ-unstable features in IBM2 χπ and χν were (-1.3 and 0.7) which signified similarity with IBM1 expected.130Ba isotope described to be transitional nucleus, transitional between SU(3) and O(6) features.

Relation between transition density and proton inelastic scattering by C12 target at Ep=65 and 200 MeV

We calculate proton elastic and inelastic scatterings with a microscopic coupled channel (MCC) calculation. The localized diagonal and coupling potentials including the spin-orbit part are obtained by folding a complex $G$-matrix effective nucleon-nucleon interaction with a transition density. This is the first time that the present folding prescription for the spin-orbit part is applied to the proton inelastic scattering, while for the monopole transition only. We apply the MCC calculation to the proton elastic and inelastic $({0}_{2}^{+})$ scatterings by $^{12}\mathrm{C}$ target at ${E}_{p}=65 \mathrm{and} 200 \mathrm{MeV}$. The role of diagonal and coupling potentials for the central and spin-orbit parts is checked. In addition, the relation between the transition density and the proton inelastic scattering is investigated with the modified wave function and the modified transition density. Namely, we perform the investigation with the artificial drastic change rather than fine structural change. The inelastic cross section is sensitive to the strength and shape of the transition density, but the inelastic analyzing power is sensitive only to the shape of that. Finally, we make clear the property of the inelastic analyzing power derived from the transition density without an ambiguity.