Valence-space In-medium Similarity Renormalization Group Research Articles

Nuclear Charge Radii of Silicon Isotopes.

The nuclear charge radius of ^{32}Si was determined using collinear laser spectroscopy. The experimental result was confronted with abinitio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of ^{32}Si completes the radii of the mirror pair ^{32}Ar-^{32}Si, whose difference was correlated to the slope L of the symmetry energy in the nuclear equation of state. Our result suggests L≤60 MeV, which agrees with complementary observables.

Ground-state mass of 22Al and test of state-of-the-art ab initio calculations* *Supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000), the CAS Project for Young Scientists in Basic Research (YSBR-002), the National Nature Science Foundation of China (12135017, 12121005, 11975280, 12105333, 12205340, 12322507, 12305126, 12305151), the Gansu Natural Science Foundation (22JR5RA123, 23JRRA614) and the

The ground-state mass excess of the drip-line nucleus Al is measured for the first time as keV using the newly-developed B ρ-defined isochronous mass spectrometry method at the cooler storage ring in Lanzhou. The new mass excess value allowed us to determine the excitation energies of the two low-lying states in Al with significantly reduced uncertainties of 51 keV. When compared to the analogue states in its mirror nucleus F, the mirror energy differences of the two states in the Al- F mirror pair are determined to be keV and keV. The excitation energies and mirror energy differences are used to test the state-of-the-art ab initio valence-space in-medium similarity renormalization group calculations with four sets of interactions derived from the chiral effective field theory. The mechanism leading to the large mirror energy differences is investigated and attributed to the occupation of the orbital.

Ab initio calculations for well deformed nuclei: 40Mg and 42Si

We performed ab initio valence-space in-medium similarity renormalization group calculations based on chiral nucleon-nucleon and three-nucleon interactions to study the neutron-rich nuclei around N=28, where the experimental and theoretical evidence point to a rapid transition from spherical to rotational regimes. First, the rotational spectra of 40Mg, 42Si, and 44S are established theoretically, anchored by the calculated E2 transition strength. The results suggest that 40Mg and 42Si exhibit large deformations. After that, the erosion of the N=28 shell closure, especially the evolutions of shape deformation and the emergence of shape coexistence, are discussed in N=28 even-even isotones ranging from 40Mg to 48Ca. Finally, the shell evolution of N=28 in Mg and Si chains is discussed based on the experimental and predicted excitation energies of low-lying states. The results from our ab initio calculations align well with available experimental data, furnishing essential insights into the structure of neutron-rich nuclei, particularly deformations in the vicinity of 40Mg and 42Si.

Electromagnetic moments of the antimony isotopes 112−133Sb

Nuclear moments of the antimony isotopes 113−133Sb are measured by collinear laser spectroscopy and used to benchmark phenomenological shell-model and ab initio calculations in the valence-space in-medium similarity renormalization group (VS-IMSRG). The shell-model calculations reproduce the electromagnetic moments over all Sb isotopes when suitable effective g-factors and charges are employed. Good agreement is achieved by VS-IMSRG for magnetic moments on the neutron-deficient side for both odd-even and odd-odd Sb isotopes while its results deviate from experiment on the neutron-rich side. When the same effective g-factors are used, VS-IMSRG agrees with experiment nearly as well as the shell model. Hence, the wave functions are very similar in both approaches and missing contributions to the M1 operator are identified as the cause of the discrepancy of VS-IMSRG with experiment. Electric quadrupole moments remain more challenging for VS-IMSRG.

Ab initio calculations of mirror energy difference in sd-shell nuclei* *Supported by the National Natural Science Foundation of China (12205340, 11975282); the Gansu Natural Science Foundation (22JR5RA123); the Special Research Assistant Project of the Chinese Academy of Sciences; the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000); the Key Research Program of the Chinese Academy of Sciences (XDPB15);

Mirror energy difference is a key observable in isospin symmetry breaking, containing rich information about nuclear structure. Understanding the mechanisms underlying mirror energy difference is important in nuclear physics. In the present work, we extensively investigated mirror energy difference using ab initio valence-space in-medium similarity renormalization group approach, focusing specifically on -shell nuclei. The low-lying spectra of Al isotopes and isotones, together with their mirror nuclei, were calculated, followed by a systematic analysis of the evolution of the mirror energy difference. The results suggest that the large mirror energy difference is mainly caused by the weakly-bound effects and large average occupations of the orbit. Lastly, we compare the results of our ab initio calculations with shell model results, elucidating the relationship and coherence between these two models.

Ab initio calculation of muon capture on Mg24

In this work we study ordinary muon capture (OMC) on $^{24}$Mg from a first principles perspective. Starting from a particular two- and three-nucleon interaction derived from chiral effective field theory, we use the valence-space in-medium similarity renormalization group (VS-IMSRG) framework to construct effective Hamiltonians and muon-capture operators which nonperturbatively account for many-body physics outside the valence space. The obtained nuclear matrix elements are compared against those from the phenomenological shell model. The impact of including the correlations from the nuclear shell model (NSM) as well as including the induced two-body part is studied in detail. Furthermore, the effects of realistic bound-muon wave function on the operators is studied. Finally, predictions for capture rates to the lowest excited states in $^{24}$Na are given and compared with available data. It is found that the spectroscopic properties of $^{24}$Mg and its OMC daughter $^{24}$Na are fairly well described by both the NSM and VS-IMSRG, and that the effect of the hadronic two-body currents significantly reduces the OMC rates. Both models have some difficulties in matching the measured OMC rates, especially for the $2^+$ final states. This calls for further studies in other light nuclei with available OMC data.

Investigation of isospin-symmetry breaking in mirror energy difference and nuclear mass with ab initio calculations

Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium-mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of $sd$- and $pf$-shell nuclei are computed for that matter. The effects of single-particle states on weakly bound and unbound nuclear states, especially those of the $s$ wave, are discussed. Predictions are also made concerning proton drip-line nuclei bearing large mirror energy difference. Finally, the coefficient of the isobaric multiplet mass equation in $T=1/2$ and $T=1$ isospin multiplets for $A=18$ to $A=76$ is calculated.

Nuclear moments of indium isotopes reveal abrupt change at magic number 82.

In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular 'magic' numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics3-5. The indium isotopes are considered a textbook example of this phenomenon6, in which the constancy of their electromagnetic properties indicated that a single unpaired proton hole can provide the identity of a complex many-nucleon system6,7. Here we present precision laser spectroscopy measurements performed to investigate the validity of this simple single-particle picture. Observation of an abrupt change in the dipole moment at N = 82 indicates that, whereas the single-particle picture indeed dominates at neutron magic number N = 82 (refs. 2,8), it does not for previously studied isotopes. To investigate the microscopic origin of these observations, our work provides a combined effort with developments in two complementary nuclear many-body methods: ab initio valence-space in-medium similarity renormalization group and density functional theory (DFT). We find that the inclusion of time-symmetry-breaking mean fields is essential for a correct description of nuclear magnetic properties, which were previously poorly constrained. These experimental and theoretical findings are key to understanding how seemingly simple single-particle phenomena naturally emerge from complex interactions among protons and neutrons.

Electromagnetic moments of scandium isotopes and N = 28 isotones in the distinctive 0f7/2 orbit

The electric quadrupole moment of 49Sc was measured by collinear laser spectroscopy at CERN-ISOLDE to be Qs=−0.159(8)eb, and a nearly tenfold improvement in precision was reached for the electromagnetic moments of 47,49Sc. The single-particle behavior and nucleon-nucleon correlations are investigated with the electromagnetic moments of Z=21 isotopes and N=28 isotones as valence neutrons and protons fill the distinctive 0f7/2 orbit, respectively, located between magic numbers, 20 and 28. The experimental data are interpreted with shell-model calculations using an effective interaction, and ab-initio valence-space in-medium similarity renormalization group calculations based on chiral interactions. These results highlight the sensitivity of nuclear electromagnetic moments to different types of nucleon-nucleon correlations, and establish an important benchmark for further developments of theoretical calculations.

Systematics of E2 strength in the sd shell with the valence-space in-medium similarity renormalization group

Background: Recent developments in {\it ab initio} nuclear theory demonstrate promising results in medium- to heavy-mass nuclei. A particular challenge for many of the many-body methodologies, however, is an accurate treatment of the electric-quadrupole, $E2$, strength associated with collectivity. Purpose: The valence-space in-medium similarity renormalization group (VS-IMSRG) is a particularly powerful method for accessing medium- and high-mass nuclei but has been found to underpredict $E2$ strengths. The purpose of this work is to evaluate the isospin dependence of this underprediction. Methods: We perform a systematic comparison of valence-space in-medium similarity renormalization group (VS-IMSRG) calculations with available literature. We make use of isoscalar and isovector contributions to the $E2$ matrix elements to assess isoscalar and isovector contributions to the missing strength. Results: It is found that the $E2$ strength is consistent throughout $T_z=\left|\frac{1}{2}\right|$, $T_z=\left|1\right|$, $T_z=\left|\frac{3}{2}\right|$ and $T_z=2$ pairs within the $sd$-shell. Furthermore, no isovector contribution to the deficiency is identified. Conclusions: A comparison with toy-models and coupled-cluster calculations is used to discuss potential origins of the missing strength, which arises from missing many-particle, many-hole excitations out of the model space. The absence of any significant isovector contribution to the missing $E2$ strength indicates that the $E2$ strength discrepancy, and therefore any correction, is largely independent of the isospin of the nuclei in question.

Coulomb excitation of the |Tz|=12, A=23 mirror pair

Background: Electric-quadrupole ($E2$) strengths relate to the underlying quadrupole deformation of a nucleus and present a challenge for many nuclear theories. Mirror nuclei in the vicinity of the line of $N=Z$ represent a convenient laboratory for testing deficiencies in such models, making use of the isospin-symmetry of the systems. Purpose: Uncertainties associated with literature $E2$ strengths in \textsuperscript{23}Mg are some of the largest in $T_z=\left|\frac{1}{2}\right|$ nuclei in the $sd$-shell. The purpose of the present work is to improve the precision with which these values are known, to enable better comparison with theoretical models. Methods: Coulomb-excitation measurements of $^{23}$Mg and $^{23}$Na were performed at the TRIUMF-ISAC facility using the TIGRESS spectrometer. They were used to determine the $E2$ matrix elements of mixed $E2$/$M1$ transitions. Results: Reduced $E2$ transition strengths, $B(E2)$, were extracted for \textsuperscript{23}Mg and \textsuperscript{23}Na. Their precision was improved by factors of approximately six for both isotopes, while agreeing within uncertainties with previous measurements. Conclusions: A comparison was made with both shell-model and {\it ab initio} valence-space in-medium similarity renormalization group calculations. Valence-space in-medium similarity-renormalization-group calculations were found to underpredict the absolute $E2$ strength - in agreement with previous studies.

Decay spectroscopy of Sc50 and Sc50m to Ti50

The $\beta$ decay of the isomeric and ground state of $^{50}$Sc to the semi-magic nucleus $^{50}_{22}$Ti$_{28}$ has been studied using a $^{50}$Ca beam delivered to the GRIFFIN $\gamma$-ray spectrometer at the TRIUMF-ISAC facility. $\beta$-decay branching ratios are reported to 16 excited states with a total of 38 $\gamma$-ray transitions linking them. These new data significantly expands the information available over previous studies. Relative intensities are measured to less than 0.001$\%$ that of the strongest transition with the majority of $\gamma$-ray transitions observed here in $\beta$ decay for the first time. The data are compared to shell-model calculations utilizing both phenomenologically-derived interactions employed in the ${\it pf}$ shell as well as a state-of-the-art, ${\it ab~initio}$ based interaction built in the valence-space in-medium similarity renormalization group framework.

Testing isospin symmetry breaking in ab initio nuclear theory

In this work we present the first steps towards benchmarking isospin symmetry breaking in ab initio nuclear theory for calculations of superallowed Fermi $\beta$-decay. Using the valence-space in-medium similarity renormalization group, we calculate b and c coefficients of the isobaric multiplet mass equation, starting from two different Hamiltonians constructed from chiral effective field theory. We compare results to experimental measurements for all T=1 isobaric analogue triplets of relevance to superallowed $\beta$-decay for masses A=10 to A=74 and find an overall agreement within approximately 250 keV of experimental data for both b and c coefficients. A greater level of accuracy, however, is obtained by a phenomenological Skyrme interaction or a classical charged-sphere estimate. Finally, we show that evolution of the valence-space operator does not meaningfully improve the quality of the coefficients with respect to experimental data, which indicates that higher-order many-body effects are likely not responsible for the observed discrepancies.

Effects of three-nucleon force on the low-lying states of <sup>28</sup>F and<sup>29</sup>Ne within <italic>ab initio</italic> calculations

One of the most interesting anomalies in nuclear physics is the island of inversion (IOI), which indicates that the magic numbers disappear. It provides a good platform to understand single-particle motion, many-body correlation, and nucleon-nucleon interaction. In neutron-rich isotopes near N =20 area, many experiments have found that the spectra, electromagnetic transitions, radii, and two-neutron separation energies of these nuclei are abnormal. This region is called the N =20 IOI, because it is characterized by neutron particle-hole excitations related to deformation from the 1s0d shell into the 1p0f shell across the N =20 shell gap. Recent experiments show that the ground states of 29Ne and 28F have negative parities, indicating that these two nuclei are within the N =20 IOI. This provides new opportunities and challenges for theoretical models in this area. With the standard shell model, the N =20 IOI has been proved by many works to have a strong cross-shell effect between 1s0d and 1p0f shells. They proposed that the tensor force and three-nucleon force should have an important influence on the microscopic description of neutron-rich nuclei in this area, especially in Ne and Mg isotopes. However, the N =20 IOI is still rarely studied in ab initio calculations. Recently, an extension of the ab initio valence-space in-medium similarity renormalization group method was presented to study the physics of neutron-rich nuclei by Miyagi et al. In the present paper, based on chiral force including nucleon-nucleon and three-nucleon force, we have performed ab initio calculations for the low-lying states of 28F and 29Ne, focusing on the relative excitation energies of the positive- and negative-parity states in these nuclei. In order to study the effect of three-nucleon force on the N =20 IOI, we use nucleon-nucleon force at N3LO with or without three-nucleon force at N2LO in our calculations. Using the open-shell many-body perturbation theory, the cross shell sd-pf realistic effective Hamiltonian, including single-particle energies and effective two-body interactions, is constructed self-consistently without introducing parameters. The constructed effective Hamiltonian is diagonalized with the shell model method. In shell model calculation, we use a truncation with up to five nucleons (including protons and neutrons) occupying the pf orbit. The low-lying states of 28F and 29Ne are calculated with NN and NN+3N interactions. The results show that three-nucleon force is important in the descriptions of low-lying states of 28F and 29Ne, especially in 29Ne while the first negative state turned to be ground state due to the three-nucleon force. Our calculations give that three-nucleon force gives large effects for the relative position between the 0d3/2 and 1p3/2 single-particle orbitals, causing the two orbitals to reverse. Furthermore, the configurations of low-lying states of 28F and 29Ne are calculated within our ab initio calculations with NN+3N interaction. The results give that the lowest positive and negative parity states in 28F and 29Ne are dominated by 2 ℏ ω and 1 ℏ ω components, respectively. We have also calculated the configurations of the ground state in neutron-rich even-even Ne isotopes, and the results indicate that the three-nucleon force could enhance the cross-shell excitations in the nuclei in the vicinity of IOI, which is essential for the exotic properties of these nuclei. Furthermore, we have also performed the phenomenological shell model calculations with SDPF-MU effective interactions, and the results are similar to our ab initio calculations including three-nucleon force.

High-resolution laser spectroscopy of Al27–32

Hyperfine spectra of $^\text{27-32}$Al ($Z=13$) have been measured at the ISOLDE-CERN facility via collinear laser spectroscopy using the $3s^23p\ ^2\text{P}^\text{o} _{3/2}\rightarrow 3s^24s\ ^2\text{S}_{1/2}$ atomic transition. For the first time, mean-square charge radii of radioactive aluminum isotopes have been determined alongside the previously unknown magnetic dipole moment of $^{29}$Al and electric quadrupole moments of $^{29,30}$Al. A potentially reduced charge radius at $N=19$ may suggest an effect of the $N=20$ shell closure, which is visible in the Al chain, contrary to other isotopic chains in the $sd$ shell. The experimental results are compared to theoretical calculations in the framework of the valence-space in-medium similarity renormalization group using multiple sets of two and three-nucleon forces from chiral effective field theory. While the trend of experimental magnetic dipole and electric quadrupole moments is well reproduced, the absolute values are underestimated by theory, consistent with earlier studies. Moreover, both the scale and trend of the charge radii appear to be very sensitive to the chosen interaction.

AbInitio Limits of Atomic Nuclei.

We predict the limits of existence of atomic nuclei, the proton and neutron drip lines, from the light through medium-mass regions. Starting from a chiral two- and three-nucleon interaction with good saturation properties, we use the valence-space in-medium similarity renormalization group to calculate ground-state and separation energies from helium to iron, nearly 700 isotopes in total. We use the available experimental data to quantify the theoretical uncertainties for our abinitio calculations towards the drip lines. Where the drip lines are known experimentally, our predictions are consistent within the estimated uncertainty. For the neutron-rich sodium to chromium isotopes, we provide predictions to be tested at rare-isotope beam facilities.

Ab initio multishell valence-space Hamiltonians and the island of inversion

In the shell-model framework, valence-space Hamiltonians connecting multiple major-oscillator shells are of key interest for investigating the physics of neutron-rich nuclei, which have been the subject of intense experimental activity for decades. Here we present an extension of the ab initio valence-space in-medium similarity renormalization group which allows the derivation of such Hamiltonians nonperturbatively. Starting from initial two- and three-nucleon forces from chiral effective field theory, we then calculate properties of nuclei in the important island-of-inversion region above oxygen, so far unexplored with ab initio methods. Our results in the neon and magnesium isotopes indicate the importance of neutron excitation from the $sd$ to $pf$ shells and ground states dominated by intruder configurations around $N=20$, consistent with the conclusions from phenomenological studies. We also benchmark the excitation spectrum of $^{16}$O with coupled-cluster theory, finding generally good agreement, and discuss implications for ground state energies and charge radii in oxygen and calcium isotopes. Finally we outline the proper procedure for treating the long-standing issue of center-of-mass contamination, and show that with a particular choice of valence space, these spurious states can be removed successfully.

Measurement and microscopic description of odd\u2013even staggering of charge radii of exotic copper isotopes

Nuclear charge radii globally scale with atomic mass number A as A1∕3, and isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. This odd–even staggering, ubiquitous throughout the nuclear landscape1, varies with the number of protons and neutrons, and poses a substantial challenge for nuclear theory2–4. Here, we report measurements of the charge radii of short-lived copper isotopes up to the very exotic 78Cu (with proton number Z = 29 and neutron number N = 49), produced at only 20 ions s–1, using the collinear resonance ionization spectroscopy method at the Isotope Mass Separator On-Line Device facility (ISOLDE) at CERN. We observe an unexpected reduction in the odd–even staggering for isotopes approaching the N = 50 shell gap. To describe the data, we applied models based on nuclear density functional theory5,6 and A-body valence-space in-medium similarity renormalization group theory7,8. Through these comparisons, we demonstrate a relation between the global behaviour of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects, naturally emerge from A-body calculations fitted to properties of A ≤ 4 nuclei.

First Glimpse of the N=82 Shell Closure below Z=50 from Masses of Neutron-Rich Cadmium Isotopes and Isomers.

We probe the N=82 nuclear shell closure by mass measurements of neutron-rich cadmium isotopes with the ISOLTRAP spectrometer at ISOLDE-CERN. The new mass of ^{132}Cd offers the first value of the N=82, two-neutron shell gap below Z=50 and confirms the phenomenon of mutually enhanced magicity at ^{132}Sn. Using the recently implemented phase-imaging ion-cyclotron-resonance method, the ordering of the low-lying isomers in ^{129}Cd and their energies are determined. The new experimental findings are used to test large-scale shell-model, mean-field, and beyond-mean-field calculations, as well as the abinitio valence-space in-medium similarity renormalization group.

Testing ab initio nuclear structure in neutron-rich nuclei: Lifetime measurements of second 2+ state in C16 and O20

To test the predictive power of ab initio nuclear structure theory, the lifetime of the second 2+ state in neutron-rich 20O, tau(2+_2 ) = 150(+80-30) fs, and an estimate for the lifetime of the second 2+ state in 16C have been obtained, for the first time. The results were achieved via a novel Monte Carlo technique that allowed us to measure nuclear state lifetimes in the tens-to-hundreds femtoseconds range, by analyzing the Doppler-shifted gamma-transition line shapes of products of low-energy transfer and deep-inelastic processes in the reaction 18O (7.0 MeV/u) + 181Ta. The requested sensitivity could only be reached owing to the excellent performances of the AGATA gamma-tracking array, coupled to the PARIS scintillator array and to the VAMOS++ magnetic spectrometer. The experimental lifetimes agree with predictions of ab initio calculations using two- and three-nucleon interactions, obtained with the valence-space in-medium similarity renormalization group for 20O, and with the no-core shell model for 16C. The present measurement shows the power of electromagnetic observables, determined with high-precision gamma spectroscopy, to assess the quality of first-principles nuclear structure calculations, complementing common benchmarks based on nuclear energies. The proposed experimental approach will be essential for short lifetimes measurements in unexplored regions of the nuclear chart, including r-process nuclei, when intense ISOL-type beams become available.