Charge radii of5556Ni reveal a surprisingly similar behavior at N 28in Ca and Ni isotopes Felix Sommer_2

2025-04-30 1 0 683.2KB 12 页 10玖币

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Charge radii of 55,56Ni reveal a surprisingly similar behavior at N= 28 in Ca and Ni

isotopes

Felix Sommer ,1, ∗Kristian K¨onig ,2Dominic M. Rossi ,1, 3 Nathan Everett,2, 4 David Garand,2

Ruben P. de Groote,5Jason D. Holt ,6, 7 Phillip Imgram,1Anthony Incorvati,2, 4 Colton Kalman,2, 8

Andrew Klose,9Jeremy Lantis ,2, 8 Yuan Liu,10 Andrew J. Miller,2, 4 Kei Minamisono ,2, 4, †

Takayuki Miyagi ,1, 11, 6 Witold Nazarewicz ,12, 4 Wilfried N¨ortersh¨auser ,1, 13, ‡Skyy V.

Pineda ,2, 8 Robert Powel,2, 4 Paul-Gerhard Reinhard,14 Laura Renth,1Elisa Romero-Romero,10, 15

Robert Roth,1, 13 Achim Schwenk ,1, 11, 16 Chandana Sumithrarachchi,2and Andrea Teigelh¨ofer6

1Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, 64289 Darmstadt, Germany

2National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA

3GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt, Germany

4Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

5Department of Physics, University of Jyv¨askyl¨a, Survontie 9, Jyv¨askyl¨a, FI-40014, Finland

6TRIUMF 4004 Wesbrook Mall, Vancouver BC V6T 2A3, Canada

7Department of Physics, McGill University, Montr´eal, QC H3A 2T8, Canada

8Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA

9Department of Chemistry, Augustana University, Sioux Falls, South Dakota 57197, USA

10Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

11ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, D-64291 Darmstadt, Germany

12Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA

13Helmholtz Research Academy Hesse for FAIR, Campus Darmstadt, 64289 Darmstadt, Germany

14Institut f¨ur Theoretische Physik II, Universit¨at Erlangen-N¨urnberg, 91058 Erlangen, Germany

15Department of Physics and Astronomy, University of Tennessee, Knoxville, Knoxville, Tennessee 37996, USA

16Max-Planck-Institut f¨ur Kernphysik, D-69117 Heidelberg, Germany

(Dated: October 6, 2022)

Nuclear charge radii of 55,56Ni were measured by collinear laser spectroscopy. The obtained

information completes the behavior of the charge radii at the shell closure of the doubly magic

nucleus 56Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly

similar despite the fact that the 56Ni core is supposed to be much softer than the 48Ca core. The

very low magnetic moment µ(55Ni) = −1.108(20) µNindicates the impact of M1 excitations between

spin-orbit partners across the N, Z = 28 shell gaps. Our charge-radii results are compared to ab

initio and nuclear density functional theory calculations, showing good agreement within theoretical

uncertainties.

Introduction. — After seventy years, the concept of

closed nuclear shells of protons and neutrons at so-called

magic numbers is still a backbone of nuclear structure

theory. The traditional magic numbers are based on

properties of nuclei at or close to the valley of β-stability.

With excursions into the exotic regions of the nuclear

landscape, a modern understanding of magic numbers

has been established. The evolution of shell gap sizes

can lead to dramatic modiﬁcations of magic numbers in

isotopes with extreme neutron-to-proton ratios [1–3].

One of the ﬁngerprints of a shell closure is a character-

istic kink in the trend of charge radii along an isotopic

chain. The origin of this kink and its relation to the

strength of a shell closure is, however, still under debate

[4–8]. Kinks in charge radii have been observed at all

neutron shell closures for which data are available with

the exception of the N= 20 neutron shell closure, where

∗fsommer@ikp.tu-darmstadt.de

†minamisono@nscl.msu.edu

‡wnoertershaeuser@ikp.tu-darmstadt.de

it has been studied so far only for Ar, K and Ca [9–11].

While N= 32 in the Ca region has been proposed to

become a magic number based on the observations of a

sudden decrease in their binding energy beyond N= 32

[12,13] and the high excitation energy of the ﬁrst excited

state in 52Ca [14], this is not supported by the behavior

of the charge radii in K across N= 32 and binding ener-

gies [15]. Indeed, N= 32 seems to be consistent with a

local neutron sub-shell closure.

A comparison of the change in mean-square charge ra-

dius, δr2

c, across a neutron shell closure for several iso-

tones reveals a remarkable similarity for the neutron shell

closures at N= 28, 50, 82, and 126. [8,16]. The evolu-

tion of δr2

cabove N= 28 is already established for

K, Ca, Mn and Fe isotopes [15,17–19] and are indeed

very similar [20]. A measurement of the charge radius of

56Ni provides essential data to study trends in δr2

cfor

two doubly magic nuclei with the same neutron magic

gap, of which the neutron-rich 48Ca is known to have

a fairly strong N= 28 shell closure [21]. In contrast,

the neutron-deﬁcient 56Ni is believed to be a rather soft

core because of its high B(E2) value [21–23] and the nu-

arXiv:2210.01924v1 [nucl-ex] 4 Oct 2022

clear magnetic moments of neighboring isotopes [24–30]

which are inconsistent with single-particle estimates. In

fact, the measured B(E2; 2+

1→0+

1) value in 48Ca (1.7

W.u.) is signiﬁcantly below that in 56Ni (7.1 W.u.) [31].

The diﬀerent nature of the proton shell-closure in Ca (the

lower πf spin-orbit partner is occupied; spin-unsaturated

regime) and Ni (both πf spin-orbit partners are occupied;

spin-saturated regime), as well as diﬀerent dynamics of

the neutron single-particle energies caused by the tensor

interaction [32] when ﬁlling the πf7

/2orbits between Ca

and Ni [3] make the comparison between the charge radii

and magnetic moments in these isotopic chains particu-

larly interesting.

Here, we report the determination of the nuclear charge

radii of 54,55,56Ni and the magnetic moment of 55Ni. In

combination with previously published data [33–35], this

establishes the behavior of δr2

cat and across the N=

28 shell closure. The measured magnetic moment of 55Ni

corrects the previous β-NMR measurement [24].

Similar to the doubly magic 40,48Ca (see, e.g., Ref.

[36]), the nuclear charge radius of 56Ni is also an ex-

cellent benchmark for ab initio nuclear structure theory.

Diﬀerent approaches have predicted the size of this nu-

cleus [37–39] and this Letter contributes new results for

this important observable.

Experiment. — Ions of 54,55,56Ni were produced at the

National Superconducting Cyclotron Laboratory (NSCL)

at Michigan State University (MSU) and collinear laser

spectroscopy (CLS) was performed at the BECOLA fa-

cility [40]. The radioactive nickel isotopes were pro-

duced through fragmentation of a 160 MeV/u primary

58Ni beam impinging on a Be target and separated

from other reaction products in the A1900 fragment

separator [41]. The particles were stopped and ther-

malized in a gas-stopper cell [42]. The extracted Ni+

ions were then accelerated to a kinetic beam energy of

30 keV and transported to the BECOLA facility with

rates of approximately 4.5×103and 6 ×103ions/s for

56Ni and 55Ni, respectively [43]. Here, a radio-frequency

quadrupole cooler and buncher (RFQ) [44] was used to

trap and cool either the radioactive beam or, for ref-

erence measurements, the stable nickel isotopes from a

local penning ionization gauge (PIG) ion source [45].

Bunches of ions were released from the RFQ into the

CLS beamline with an eﬃciency of 70% at ion ener-

gies of Eion ≈29 850 eV and were collinearly superim-

posed with the spectroscopy laser light and guided into

the charge-exchange cell [46,47] loaded with sodium and

heated to 420 °C. Under these conditions, a neutraliza-

tion eﬃciency of typically 50 % was achieved of which

an estimated fraction of 15% populates the lower level of

the atomic 3d94s3

D3→3d94p3

P2transition at 352 nm.

Resonance spectra were recorded by changing a small

voltage applied to the charge-exchange cell to Doppler-

tune the laser frequency in the rest-frame of the atoms.

The laser frequency was adjusted for each isotope to keep

the central acceleration voltage almost identical. Fluo-

rescence photons were detected with three consecutive

photo-multiplier tubes mounted on chambers with diﬀer-

ent mirror geometries [48,49]. The laser light of 352 nm

was generated in a frequency-doubling cavity (Wave-

train, Spectra Physics) from the output of a continuous-

wave titanium-sapphire (Ti:Sa) laser (Matisse TS, Sirah

Lasertechnik) operated at 704 nm. The Ti:Sa output was

measured and stabilized by a wavemeter (WSU30, High-

Finesse), which in turn was calibrated to a frequency

stabilized helium-neon laser (SL 03, SIOS Messtechnik)

once every minute.

A pair of reference measurements of 58,60Ni isotopes

from the oﬀ-line PIG source was conducted typically once

every 6–12 hours. These reference measurements were

used to determine the isotope shifts of the short-lived

54−56Ni isotopes with respect to 60Ni and also allowed to

calibrate the ion energy to the known absolute transition

frequency of 60Ni [50].

Results. — The resonance spectra of the measured

nickel isotopes are shown in Fig. 1, together with a Voigt

lineshape ﬁtted to each dataset. Energy losses from in-

elastic collisions in the charge-exchange cell lead to an

asymmetric lineshape that was modelled by including one

additional, smaller Voigt proﬁle into the ﬁt function at

a phenomenologically determined lower ion energy [46].

The spectra of stable 56,58,60Ni isotopes were ﬁtted sep-

arately for each measurement, whereas the events of all

54,55Ni data sets were summed up before the ﬁtting pro-

cedure due to lower production yields. Details regarding

the ﬁtting of the 55Ni spectrum are given in the Supple-

mental Material (Suppl. Mat.) [43].

The isotope shift δνA,60 =νA−ν60 for each isotope

ANi relative to 60Ni was calculated from the extracted

centroid frequencies. For the low-production isotopes

54Ni and 55Ni, the uncertainties of the isotope shifts are

dominated by the ﬁt uncertainty of their centroid posi-

tions. For 56Ni and the stable 58Ni, uncertainties of the

frequency measurements [50] and an observed deviation

between bunched-beam and continuous-beam measure-

ments [51] are the prevailing contributions to the isotope-

shift uncertainties.

The diﬀerential mean-square (ms) charge radii δr2

c

were determined as

δr2

cA,A0

=δνA,A0

−Kα·µA,A0

F+α·µA,A0,(1)

where Kαand Fare the so called mass- and ﬁeld-shift

factors, respectively, and µA,A0= (mA−mA0)/(mA+

me)(mA0+me) is the mass-scaling factor. A constant

factor α= 388 GHz u shifts the abscissa to remove the

correlation between Kand F[52]. The factors Kα=

954(4) GHz u and F=−805(66) MHz/fm2were deter-

mined in a King plot procedure by comparing the iso-

tope shifts of stable nickel isotopes, measured oﬀ-line

at BECOLA, with their known diﬀerential charge radii

FIG. 1. Sum spectra of proton-rich, radioactive nickel iso-

topes 54,55,56Ni and of the reference isotopes 58,60Ni measured

at BECOLA. The solid red lines show the ﬁts to the data

and the centers of gravity (c.o.g.) for each spectrum are de-

picted as dashed blue lines. While the displayed counts are

close to the actually observed numbers, deviations occur due

to the normalization procedure used to combine all data of

the beamtime in these spectra. Only the measured part of

the 55Ni hyperﬁne spectrum is shown. For more details, see

Suppl. Mat. [43].

from literature [53]. This King ﬁt analysis is detailed in

[51]. The total root-mean-square (rms) charge radii Rc

were then determined with respect to the reference value

Rc(60Ni) [53]. The isotope shifts, diﬀerential ms charge

radii, and rms charge radii are summarized in Tab. I.

The values of charge radii along the 54Ni – 58Ni iso-

topes establish the behavior of nickel charge radii across

the N=Z= 28 doubly-magic shell closure, and the

value of 55Ni provides information on odd-even stagger-

ing in the neutron f7

/2shell. The charge radius of 57Ni,

which could yield further insight to the odd-even stagger-

ing, has so far neither been obtained in literature nor has

it been measured at BECOLA. Our result for 58Ni agrees

well with the previous measurements from Refs. [33] and

[54]. Furthermore, the nuclear magnetic dipole moment

of the I=7

2[55] isotope 55Ni was determined from the

upper and lower hyperﬁne A-factors as listed in Tab. II.

The Suppl. Mat. [43] contains a more detailed descrip-

TABLE I. Isotope shifts, diﬀerential ms charge radii, and ab-

solute rms charge radii for all nickel isotopes investigated at

BECOLA. Uncertainties in parentheses denote combined un-

correlated uncertainties of statistical and systematic nature,

whereas those in square brackets are correlated through the

uncertainty of the King-plot parameters, which are taken from

[51] and given in the text.

δνA,60/MHz δr2

cA,60 /fm2Rc(ANi)/fm

54Ni −1919.7(7.9) −0.522(9)[19] 3.7366(13)[31]

55Ni −1426.9(19.1) −0.607(23)[09] 3.7252(32)[21]

56Ni −1002.7(3.8) −0.626(02)[16] 3.7226(03)[27]

58Ni −506.3(2.5) −0.276(01)[06] 3.7695(02)[19]

60Ni 0 0 3.8059[17]

tion of the ﬁtting procedure for 55Ni and a discussion of

the magnetic moment, which includes Refs. [24,28,56–

59]. Our magnetic moment deviates signiﬁcantly from

the previously reported β-NMR value [24], which has

been based on a single resonance point deviating 3σfrom

the baseline. The very low magnetic moment being only

55% of the single-particle νf7

/2value indicates the im-

pact of M1 excitations between the νf spin-orbit part-

ners across the N, Z = 28 shell gap. Our value is in good

agreement with shell-model calculations with the GXPF1

interaction [24], which suggest a soft 56Ni core. This is in

contrast with 47Ca, which has a magnetic moment very

close to the eﬀective g-value established in this region

[60].

Theory. — The Ni chain and all medium-mass nuclei

can be accessed by the ab initio valence-space in-medium

similarity renormalization group (VS-IMSRG) [62–64],

which generates an approximate unitary transformation

to decouple both a valence space and associated core

from particle or hole excitations to outside conﬁgura-

tions. The VS-IMSRG many-body calculations use the

IMSRG code from [65] and follow those of Ref. [35], ex-

cept that for three-nucleon (3N) matrix elements we use

a suﬃciently large truncation [66], so that energies and

radii are converged with respect to the 3N basis size.

Our calculations are based on two-nucleon (NN) and

3N interactions from chiral eﬀective ﬁeld theory (EFT).

TABLE II. A-parameters of the hyperﬁne structure that was

ﬁtted to the 55Ni spectrum. The nuclear magnetic dipole

moment µis the weighted average of the extraction using the

upper and the lower A-factor based on the nuclear magnetic

moment of µ(61Ni) = −0.749 65(5) µN[61].

This work Lit. [24]

Alo/MHz Aup/MHz A-Ratio µ/µNµ/µN

-288.4(5.6) -112.1(4.9) 0.389(19) -1.108(20) -0.976(26)

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Chargeradiiof55;56NirevealasurprisinglysimilarbehavioratN=28inCaandNiisotopesFelixSommer,1,KristianKonig,2DominicM.Rossi,1,3NathanEverett,2,4DavidGarand,2RubenP.deGroote,5JasonD.Holt,6,7PhillipImgram,1AnthonyIncorvati,2,4ColtonKalman,2,8AndrewKlose,9JeremyLantis,2,8YuanLiu,10AndrewJ.Miller,2,4KeiM...

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Charge radii of5556Ni reveal a surprisingly similar behavior at N 28in Ca and Ni isotopes Felix Sommer_2

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