arXiv subjects

M. Scheck

Publications and source records attributed to M. Scheck.

At least 19 recordsLinked to original sources

arXiv2025

Seniority-two valence-shell building blocks of the octupole phonon

The relative ordering of $J^-$ levels of multiplets resulting from two-body excitations, which include a $J^{\pi}=3^-$ state that can contribute to the octupole phonon, are investigated in a simplistic shell-model approach. To calculate the relative level ordering, harmonic oscillator wavefunctions and a residual $\delta$ interaction are used. The simplistic approach confirms for the particle-particle channel, the often stated preference of the $\Delta j=3, \Delta l =3$ subshell combination over the $\Delta j=3, \Delta l =1$ subshell combination through an enhanced energy gain. Furthermore, it is shown that, in the particle-hole channel, the gain is less pronounced for the $\Delta j=3, \Delta l =3$ subshell configuration. In combination with the overall structure of an oscillator shell, these results explain the comparatively low excitation energy for 3$^-_1$ excitations observed for the octupole-soft proton and neutron numbers predicted by various models.

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arXiv2025

Deviations from the Porter-Thomas Distribution due to Nonstatistical $\gamma$ Decay below the $^{150}$Nd Neutron Separation Threshold

We introduce a new method for the study of fluctuations of partial transition widths based on nuclear resonance fluorescence experiments with quasimonochromatic linearly polarized photon beams below particle separation thresholds. It is based on the average branching of decays of $J=1$ states of an even-even nucleus to the $2^+_1$ state in comparison to the ground state. Between 5 and 7 MeV, a constant average branching ratio for $\gamma$ decays from $1^-$ states of 0.490(16) is observed for the nuclide $^{150}$Nd. Assuming $\chi^2$-distributed partial transition widths, this average branching ratio is related to a degree of freedom of $\nu = 1.93(12)$, rejecting the validity of the Porter-Thomas distribution, requiring $\nu=1$. The observed deviation can be explained by nonstatistical effects in the $\gamma$-decay behavior with contributions in the range of 9.4(10)% up to 94(10)%.

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arXiv2024

Shape Coexistence in $^{94}$Zr from a Model-Independent Analysis

Low-lying states of $^{94}$Zr were investigated via low-energy multi-step Coulomb excitation. From the measured $\gamma$-ray yields, \textcolor{black}{16} reduced \textcolor{black}{E2} transition probabilities between low-spin states were determined, together with the spectroscopic quadrupole moments of the $2_{1,2}^+$ states. Based on this information, for the first time in the Zr isotopic chain, the shapes of the $0_{1,2}^+$ states including their deformation softness were inferred in a model-independent way using the quadrupole sum rules approach. The ground state of $^{94}$Zr possesses a rather diffuse shape associated with a spherical configuration, while the $0_2^+$ state is \textcolor{black}{triaxial tending towards} oblate and more strongly deformed. {\color{black}The observed features of shape coexistence in $^{94}$Zr are consistent with both Monte-Carlo shell-model predictions and IBM-CM calculations, and provide model-independent constraints on the shape character assigned in the IBM-CM to the intruder configuration in $^{92\text{--}96}$Zr.}

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arXiv2024

Electric and magnetic dipole strength in $^{58}$Ni from forward-angle inelastic proton scattering

The aim of the present work is a state-by-state analysis of possible E1 and M1 transitions in $^{58}$Ni with a high-resolution (p,p') experiment at 295 MeV and very forward angles including 0{\deg} and a comparison to results from studies of the dipole strength with the $(\gamma,\gamma')$ and (e,e') reactions. The E1 and M1 cross sections of individual peaks in the spectra are deduced with a multipole decomposition analysis and converted to reduced E1 and spin-M1 transition strengths using the virtual photon and the unit cross-section method, respectively. Despite the high level density good agreement is obtained for the deduced excitation energies of J = 1 states in the three types of experiments indicating that the same states are excited. The B(E1) and B(M1) strengths from the $(\gamma,\gamma^\prime)$ experiments are systematically smaller than in the present work because of the lack of information on branching ratios to lower-lying excited states and the competition of particle emission. Fair agreement with the B(M1) strengths extracted from the (e,e') data is obtained after removal of E1 transitions uniquely assigned in the present work, which belong to a low-energy toroidal mode with unusual properties mimicking M1 excitations in electron scattering. The experimental M1 strength distribution is compared to large-scale shell-model calculations with the effective GXPF1A and KB3G interactions. They provide a good description of the isospin splitting and the running sum of the M1 strength. A quenching factor 0.74 for the spin-isospin part of the M1 operator is needed to attain quantitative agreement with the data.

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arXiv2023

Candidate toroidal electric dipole mode in the spherical nucleus $^{58}$Ni

Dipole toroidal modes appear in many fields of physics. In nuclei, such a mode was predicted more than 50 years ago, but clear experimental evidence was lacking so far. Using a combination of high-resolution inelastic scattering experiments with photons, electrons and protons, we identify for the first time candidates for toroidal dipole excitations in the nucleus $^{58}$Ni and demonstrate that transverse electron scattering form factors represent a relevant experimental observable to prove their nature.

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arXiv2022

A new avenue in the search for CP violation: Moessbauer spectroscopy of 227-Ac

This work proposes a new avenue in the search for CP-violating odd-electric and even-magnetic nuclear moments. A promising candidate to find such moments in the ground state is the quadrupole-deformed and octupole-correlated nucleus 227-actinium. In this nucleus, the 27.4-keV $E1$~transition that connects the $3/2^+$ parity-doublet partner and the $3/2^-$ ground state is perfectly suited to apply the sensitive technique of recoil-free selfabsorption, commonly known as M\"ossbauer spectroscopy. In this experimental approach, the lifetime of the $3/2^+$ upper parity-doublet partner allows an estimate of the lower limit of $\Delta E = 2\cdot \Gamma_{\gamma}$= $23.7(1) \times 10^{-9}$ eV for the achievable energy resolution to be made. This resolution must be exceeded by the interaction of a CP-violating moment and the corresponding multipole moment of the field distribution in the lattice. This work presents the first ideas for patterns caused by CP-violating moments on the expected quadrupole splitting and nuclear Zeeman effect.

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arXiv2022

Model-independent determination of the dipole response of $^{66}$Zn using quasi-monoenergetic and linearly-polarized photon beams

[Background] Photon strength functions are an important ingredient in calculations relevant for the nucleosynthesis of heavy elements. The relation to the photoabsorption cross section allows to experimentally constrain photon strength functions by investigating the photo-response of atomic nuclei. [Purpose] We determine the photoresponse of $^{66}$Zn in the energy region of 5.6 MeV to 9.9 MeV and analyze the contribution of the "elastic" decay channel back to the ground state. In addition, for the elastic channel electric and magnetic dipole transitions were separated. [Methods] Nuclear resonance fluorescence experiments were performed using a linearly-polarized quasi-monoenergetic photon beam at the High Intensity $\gamma$-ray Source. Photon beam energies from 5.6 to 9.9 MeV with an energy spread of about 3% were selected in steps of 200-300 keV. Two High Purity Germanium detectors were used for the subsequent $\gamma$-ray spectroscopy. [Results] Full photoabsorption cross sections are extracted from the data making use of the monoenergetic character of the photon beam. For the ground-state decay channel, the average contribution of electric and magnetic dipole strengths is disentangled. The average branching ratio back to the ground state is determined as well. [Conclusions] The new results indicate lower cross sections when compared to the values extracted from a former experiment using bremsstrahlung on $^{66}$Zn. In the latter, the average branching ratio to the ground state is estimated from statistical-model calculations in order to analyze the data. Corresponding estimates from statistical-model calculations underestimate this branching ratio compared to the values extracted from the present analysis, which would partly explain the high cross sections determined from the bremsstrahlung data.

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arXiv2022

Isospin Mixing and the Cubic Isobaric Multiplet Mass Equation in the Lowest T = 2, A = 32 Quintet

The isobaric multiplet mass equation (IMME) is known to break down in the first T = 2, A = 32 isospin quintet. In this work we combine high-resolution experimental data with state-of-the-art shell-model calculations to investigate isospin mixing as a possible cause for this violation. The experimental data are used to validate isospin-mixing matrix elements calculated with newly developed shell-model Hamiltonians. Our analysis shows that isospin mixing with nonanalog T = 1 states contributes to the IMME breakdown, making the requirement of an anomalous cubic term inevitable for the multiplet.

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arXiv2020

Accessing the Single-Particle Structure of the Pygmy Dipole Resonance in $^{208}$Pb

New experimental data on the neutron single-particle character of the Pygmy Dipole Resonance (PDR) in $^{208}$Pb are presented. They were obtained from $(d,p)$ and resonant proton scattering experiments performed at the Q3D spectrograph of the Maier-Leibnitz Laboratory in Garching, Germany. The new data are compared to the large suite of complementary, experimental data available for $^{208}$Pb and establish $(d,p)$ as an additional, valuable, experimental probe to study the PDR and its collectivity. Besides the single-particle character of the states, different features of the strength distributions are discussed and compared to Large-Scale-Shell-Model (LSSM) and energy-density functional (EDF) plus Quasiparticle-Phonon Model (QPM) theoretical approaches to elucidate the microscopic structure of the PDR in $^{208}$Pb.

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arXiv2020

Role of chiral two-body currents in $^6$Li magnetic properties in light of a new precision measurement with the relative self-absorption technique

A direct measurement of the decay width of the excited $0^+_1$ state of $^6$Li using the relative self-absorption technique is reported. Our value of $\Gamma_{\gamma, 0^+_1 \to 1^+_1} = 8.17(14)_\mathrm{stat.}(11)_\mathrm{syst.} \mathrm{eV}$ provides sufficiently low experimental uncertainties to test modern theories of nuclear forces. The corresponding transition rate is compared to the results of ab initio calculations based on chiral effective field theory that take into account contributions to the magnetic dipole operator beyond leading order. This enables a precision test of the impact of two-body currents that enter at next-to-leading order.

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arXiv2020

Structure of high-lying levels populated in the $^{96}$Y $\rightarrow ^{96}$Zr $\beta$ decay

The nature of $J^{\pi}=1^-$ levels of $^{96}$Zr below the $\beta$-decay $Q_{\beta}$ value of $^{96}$Y has been investigated in high-resolution $\gamma$-ray spectroscopy following the $\beta$ decay as well as in a campaign of inelastic photon scattering experiments. Branching ratios extracted from $\beta$ decay allow the absolute $E1$ excitation strength to be determined for levels populated in both reactions. The combined data represents a comprehensive approach to the wavefunction of $1^-$ levels below the $Q_{\beta}$ value, which are investigated in the theoretical approach of the Quasiparticle Phonon Model. This study clarifies the nuclear structure properties associated with the enhanced population of high-lying levels in the $^{96}$Y$_{gs}$ $\beta$ decay, one of the three most important contributors to the high-energy reactor antineutrino spectrum.

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arXiv2020

The observation of vibrating pear shapes in radon nuclei: update

There is a large body of evidence that atomic nuclei can undergo octupole distortion and assume the shape of a pear. This phenomenon is important for measurements of electric-dipole moments of atoms, which would indicate CP violation and hence probe physics beyond the standard model of particle physics. Isotopes of both radon and radium have been identified as candidates for such measurements. Here, we have observed the low-lying quantum states in $^{224}$Rn and $^{226}$Rn by accelerating beams of these radioactive nuclei. We report here additional states not assigned in our 2019 publication. We show that radon isotopes undergo octupole vibrations but do not possess static pear-shapes in their ground states. We conclude that radon atoms provide less favourable conditions for the enhancement of a measurable atomic electric-dipole moment.

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arXiv2020

Evolution of Octupole Deformation in Radium Nuclei from Coulomb Excitation of Radioactive $^{222}$Ra and $^{228}$Ra Beams

There is sparse direct experimental evidence that atomic nuclei can exhibit stable pear shapes arising from strong octupole correlations. In order to investigate the nature of octupole collectivity in radium isotopes, electric octupole ($E3$) matrix elements have been determined for transitions in $^{222,228}$Ra nuclei using the method of sub-barrier, multi-step Coulomb excitation. Beams of the radioactive radium isotopes were provided by the HIE-ISOLDE facility at CERN. The observed pattern of $E$3 matrix elements for different nuclear transitions is explained by describing $^{222}$Ra as pear-shaped with stable octupole deformation, while $^{228}$Ra behaves like an octupole vibrator.

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arXiv2019

First direct measurement of the intrinsic dipole moment in pear-shaped thorium isotopes

It is now well established that atomic nuclei composed of certain combinations of protons and neutrons can adopt reflection-asymmetric, or octupole-deformed, shapes at low excitation energy. These nuclei show promise in the search for a permanent atomic electric dipole moment, the existence of which has implications for physics beyond the Standard Model. Theoretical studies have suggested that certain isotopes of thorium may have the largest octupole deformation. However, due to experimental challenges, the extent of the octupole collectivity in the low-energy states in these thorium nuclei has not yet been demonstrated. This paper reports measurements of the lifetimes of low-energy states in 228Th (Z = 90) undertaken using the mirror symmetric centroid difference method, which is a direct electronic fast-timing technique. Lifetime measurements of the low-lying Jp = 1- and 3- states, which are the first for a thorium isotope, have allowed the B(E1) rates and the intrinsic dipole moment to be determined. The results are in agreement with those of previous theoretical calculations allowing the extent of the octupole deformation of 228Th to be estimated. This study indicates that the nuclei 229Th and 229Pa (Z = 91) may be good candidates for the search for a permanent atomic electric dipole moment.

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arXiv2017

A revised $B(E2; 2^+_1 \to 0^+_1)$ value in the semi-magic nucleus $^{210}$Po

The lifetimes of the $2^+_1$, the $2^+_2$ and the $3^-_1$ states of $^{210}$Po have been measured in the $^{208}$Pb($^{12}$C,$^{10}$Be)$^{210}$Po transfer reaction by the Doppler-shift attenuation method. The results for the lifetime of the $2^+_1$ state is about three times shorter than the adopted value. However, the new value still does not allow for consistent description of the properties of the yrast $2^+_1$, $4^+_1$, $6^+_1$, and $8^+_1$ states of $^{210}$Po in the framework of nuclear shell models. The Quasi-particle Phonon Model (QPM) calculations also cannot overcome this problem thus indicating the existence of a peculiarity which is neglected in both theoretical approaches.

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arXiv2016

Direct Evidence of Octupole Deformation in Neutron-Rich $^{144}$Ba

The neutron-rich nucleus $^{144}$Ba ($t_{1/2}$=11.5 s) is expected to exhibit some of the strongest octupole correlations among nuclei with mass numbers $A$ less than 200. Until now, indirect evidence for such strong correlations has been inferred from observations such as enhanced $E1$ transitions and interleaving positive- and negative-parity levels in the ground-state band. In this experiment, the octupole strength was measured directly by sub-barrier, multi-step Coulomb excitation of a post-accelerated 650-MeV $^{144}$Ba beam on a 1.0-mg/cm$^2$ $^{208}$Pb target. The measured value of the matrix element, $\langle 3_1^- \| \mathcal{M}(E3) \| 0_1^+ \rangle=0.65(^{+17}_{-23})$ $e$b$^{3/2}$, corresponds to a reduced $B(E3)$ transition probability of 48($^{+25}_{-34}$) W.u. This result represents an unambiguous determination of the octupole collectivity, is larger than any available theoretical prediction, and is consistent with octupole deformation.

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arXiv2015

Collectivity in the light radon nuclei measured directly via Coulomb excitation

Background: Shape coexistence in heavy nuclei poses a strong challenge to state-of-the-art nuclear models, where several competing shape minima are found close to the ground state. A classic region for investigating this phenomenon is in the region around $Z=82$ and the neutron mid-shell at $N=104$. Purpose: Evidence for shape coexistence has been inferred from $\alpha$-decay measurements, laser spectroscopy and in-beam measurements. While the latter allow the pattern of excited states and rotational band structures to be mapped out, a detailed understanding of shape coexistence can only come from measurements of electromagnetic matrix elements. Method: Secondary, radioactive ion beams of $^{202}$Rn and $^{204}$Rn were studied by means of low-energy Coulomb excitation at the REX-ISOLDE facility in CERN. Results: The electric-quadrupole ($E2$) matrix element connecting the ground state and first-excited $2^{+}_{1}$ state was extracted for both $^{202}$Rn and $^{204}$Rn, corresponding to ${B(E2;2^{+}_{1} \to 2^{+}_{1})=29^{+8}_{-8}}$ W.u. and $43^{+17}_{-12}$ W.u., respectively. Additionally, $E2$ matrix elements connecting the $2^{+}_{1}$ state with the $4^{+}_{1}$ and $2^{+}_{2}$ states were determined in $^{202}$Rn. No excited $0^{+}$ states were observed in the current data set, possibly due to a limited population of second-order processes at the currently-available beam energies. Conclusions: The results are discussed in terms of collectivity and the deformation of both nuclei studied is deduced to be weak, as expected from the low-lying level-energy schemes. Comparisons are also made to state-of-the-art beyond-mean-field model calculations and the magnitude of the transitional quadrupole moments are well reproduced.

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arXiv2014

Shape coexistence in neutron-deficient Hg isotopes studied via lifetime measurements in $^{184,186}$Hg and two-state mixing calculations

The neutron-deficient mercury isotopes, $^{184,186}$Hg, were studied with the Recoil Distance Doppler Shift (RDDS) method using the Gammasphere array and the Köln Plunger device. The Differential Decay Curve Method (DDCM) was employed to determine the lifetimes of the yrast states in $^{184,186}$Hg. An improvement on previously measured values of yrast states up to $8^{+}$ is presented as well as first values for the $9_{3}$ state in $^{184}$Hg and $10^{+}$ state in $^{186}$Hg. $B(E2)$ values are calculated and compared to a two-state mixing model which utilizes the variable moment of inertia (VMI) model, allowing for extraction of spin-dependent mixing strengths and amplitudes.

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