Exploiting dissipative reactions to perform in-beam -ray spectroscopy of the neutron-decient isotopes3839Ca A. Gade1 2D. Weisshaar1B. A. Brown1 2D. Bazin1 2K. W. Brown1 3R. J. Charity4P.

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Exploiting dissipative reactions to perform in-beam γ-ray spectroscopy of the

neutron-deﬁcient isotopes 38,39Ca

A. Gade,1, 2 D. Weisshaar,1B. A. Brown,1, 2 D. Bazin,1, 2 K. W. Brown,1, 3 R. J. Charity,4P.

Farris,1, 2 A. M. Hill,1, 2 J. Li,1B. Longfellow,1, 2, ∗D. Rhodes,1, 2, †W. Reviol,5and J. A. Tostevin6

1Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA

2Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

3Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA

4Department of Chemistry, Washington University, St. Louis, Missouri 63130, USA

5Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

6Department of Physics, Faculty of Engineering and Physical Sciences,

University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom

(Dated: October 4, 2022)

The neutron-deﬁcient Ca isotopes continue to attract attention due to their importance for testing

isospin symmetry and their relevance in capture reactions of interest for nova nucleosynthesis and

the shape of light curves in Type I X-ray bursts. To date, spectroscopic information on 38,39Ca is

largely limited to data on lower-spin excited states. Here, we report in-beam γ-ray spectroscopy

of complementary higher-spin, complex-structure states in 39 Ca populated in fast-beam-induced,

momentum-dissipative processes leading to neutron pickup onto excited conﬁgurations of the pro-

jectile, 9Be(38Ca∗,39 Ca + γ)X. Such a dissipative reaction was recently characterized for the case

of inelastic scattering of 38Ca oﬀ 9Be, 9Be(38 Ca,38 Ca + γ)X. Additional data and discussion on the

nuclear structure of 38 Ca is also presented. An explanation for the more-complex-structure states,

populated with small cross sections in one-nucleon knockout reactions, and observed in the tails of

their longitudinal momentum distributions, is also oﬀered.

I. INTRODUCTION

The study of the structure of rare isotopes is fueled

by an increasing body of complementary experimental

data that reach further and further into the territory of

high isospin. Here, changes in the nuclear structure chal-

lenge nuclear theory in the quest for a predictive model

of nuclei. Often, direct reactions or inelastic scatter-

ing processes are used in experimental studies that se-

lect single-particle or collective degrees of freedom, pre-

dominantly, providing information on low-lying states.

Complex-conﬁguration, higher-spin states near the yrast

line that may be part of collective, band-like structures,

have traditionally been accessed with fusion-evaporation

reactions on the neutron-deﬁcient side of the nuclear

chart when suitable stable projectile and target combi-

nations exist. Incomplete fusion [1] or cluster transfer

reactions in normal kinematics induced by stable beams

[2] or inverse-kinematics reactions with radioactive pro-

jectiles and light stable targets [3–5], at low beam ener-

gies, have been used in only a very few cases to access

high-spin yrast states; the latter type of studies is sparse

due to the limited availability of the intense low-energy

rare-isotope beams that are necessary.

Here, we extend the work on neutron-deﬁcient nu-

clei reported in Ref. [6] and report the in-beam

γ-ray spectroscopy of complex-structure, core-coupled

∗Present address: Lawrence Livermore National Laboratory, Liv-

ermore, California 94550, USA

†Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, BC

V6T 2A3, Canada

states near the yrast line of 39Ca. These states

were populated in fast-beam-induced, dissipative (high-

momentum-loss) reaction processes leading to single-

neutron addition onto excited conﬁgurations of the pro-

jectile, 9Be(38Ca∗,39Ca + γ)X. Complementing the anal-

ysis presented in Ref. [6], we provide further discussion

on the inelastic scattering, 9Be(38Ca,38Ca+γ)X, at high

momentum loss. Figure 1 shows the location of these

systems on the nuclear chart.

39Ti 40Ti 41Ti

39Sc 40Sc

Ca 38Ca 39Ca

Neutron number

N=20

40Ca

41Sc 42Sc

42Ti 43Ti

Proton number

34Ca 35Ca 36Ca

35K36K37K38K39

34K40

p unbound

projectile

reaction residue

stable or T1/2>1 109 yr

Ar 36Ar 37Ar 38Ar 39

32Ar 33Ar 34Ar

30Ar 31Ar

FIG. 1. Part of the nuclear chart showing the projectile beam

38Ca and the one-neutron pickup residue 39Ca in the proxim-

ity of the proton dripline.

The neutron-deﬁcient 38Ca isotope continues to attract

attention due to its importance for testing fundamen-

tal symmetries [7–13] and as the compound nucleus in

the 34Ar(α, p)37K capture reaction of relevance for X-

arXiv:2210.01106v1 [nucl-ex] 3 Oct 2022

ray bursts [14]. For nuclear structure studies, 38Ca can

be accessed via (3He,n) and (p, t) reactions from stable

36Ar and 40Ca, respectively. Hence an extensive body of

work is available on, for example, pairing vibrations [15],

fp-shell conﬁgurations [16], and an anomalous L= 0

transition to the ﬁrst excited 0+state. The latter was

observed in the (p, t) reaction from 40Ca [17–20]. The

intermediate-energy Coulomb excitation measurement by

Cottle et al. [21], exploring isospin symmetry, is the only

one using a beam of unstable 38Ca projectiles. The sole

published studies using γ-ray spectroscopy are from 1970

[22] ((3He, nγ), using three Ge(Li) detectors) and 1999

[21] (intermediate-energy Coulomb excitation, using a

NaI scintillator array). NNDC further quotes γ-ray data

from a 1974 Duke University PhD Thesis [23] which ap-

pears unpublished for all practical purposes. The data

presented here constitute the ﬁrst γ-ray spectroscopy of

38Ca exploiting a modern, high-resolution HPGe γ-ray

tracking array.

Unlike for 38Ca, modern γ-ray spectroscopy data are

available for 39Ca. For example, from (a) a recent

(3He, αγ) experiment [24], aimed at observables impor-

tant for the 38K(p, γ)39Ca reaction rate, and (b) from a

high-spin spectroscopy study via the 16O(28Si, αnγ)39Ca

reaction [25]. In the present work, we show that dis-

sipative processes in the fast-beam one-neutron pickup

channel populate the very same states as reported in the

high-spin study of Ref. [25], suggesting a possible novel

and practical pathway to study such states in rare iso-

topes. This also elucidates the observation of such states,

with low yields, in the low-momentum tails of longitudi-

nal momentum distributions in nucleon knockout exper-

iments, reported in recent measurements.

II. EXPERIMENT, RESULTS AND

DISCUSSION

The experimental details and setup are also discussed

in Refs. [6, 26] and a brief summary is provided

here. The 38Ca rare-isotope beam was produced at

the Coupled Cyclotron Facility at NSCL [27] in the

fragmentation of a stable 140-MeV/nucleon 40Ca pri-

mary beam in the A1900 fragment separator [28], on

a 799 mg/cm2 9Be production target and separated us-

ing a 300 mg/cm2Al degrader. The momentum width

was limited to ∆p/p = 0.25% for optimum resolu-

tion, resulting in 160,000 38Ca/s interacting with a 188-

mg/cm2-thick 9Be foil placed in the center of the high-

resolution γ-ray tracking array GRETINA [29, 30] sur-

rounding the reaction target position of the S800 spec-

trograph [31]. The 38Ca projectiles had a mid-target

energy of 60.9 MeV/nucleon. The incoming beam and

the projectile-like reaction residues were event-by-event

identiﬁed using the S800 analysis beam line and focal

plane [32]. The scattered 38Ca and one-neutron pickup

residues, 39Ca, are cleanly separated in the particle iden-

tiﬁcation plot displayed in Fig. 2. The magnetic rigidity

of the S800 spectrograph was tuned for the two-neutron

removal reaction to 36Ca and so only the outermost low-

momentum tails of the reacted 38Ca and 39Ca longitu-

dinal momentum distributions were transmitted to the

S800 focal plane, as quantiﬁed below. In the following,

we will ﬁrst discuss the general characteristics of the reac-

tions and then focus on the detailed spectroscopy results

for 39Ca and on additional data and discussion for 38Ca

not presented in [6].

40Sc

38Ca

36Ca

32Ar

28S

Energy loss (arb. units)

39Ca

FIG. 2. Particle identiﬁcation showing the same data as in

Fig. 2 of Ref. [26] with 38,39 Ca highlighted.

With the chosen magnetic rigidity, optimized for 36Ca,

the parts of the 39Ca and 38Ca momentum distributions

that enter the S800 focal plane are approximately ±300

MeV/c about the momentum p0= 11.222 GeV/c. Figure

3 shows the measured parallel momentum distributions

of (i) the low-momentum tail of the 38Ca distribution on

a logarithmic scale (shown as an inset), over a slightly re-

duced momentum range that is not subject to further ac-

ceptance eﬀects, and (ii) the tail of the 39Ca one-neutron

pickup distribution (purple curve) from the same setting.

This 39Ca distribution is further impacted by the focal-

plane acceptance starting at about p0+ 275 MeV/c. The

momentum distribution of the unreacted 38Ca after pas-

sage through the target is also shown (blue curve, roughly

centered on p0= 11.932 GeV/c) to help clarify the mo-

mentum losses in the observed 39Ca and 38Ca tail distri-

butions.

The parallel momentum distribution of 39Ca is cut by

the S800 focal-plane acceptance on the high-momentum

end, leaving only a tail within the acceptance. It is in-

teresting to estimate where the centroid of the full dis-

tribution would be. The complication here is that this

depends on the momentum of the neutron picked up

from the target which is not precisely calculable, given

that our reaction is highly linear-momentum mismatched

and is dominated by the pickup of deeply bound, high-

momentum neutrons [33]. Such fast-beam one-nucleon

pickup reactions have been carried out for a number of

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Exploitingdissipativereactionstoperformin-beam-rayspectroscopyoftheneutron-decientisotopes38;39CaA.Gade,1,2D.Weisshaar,1B.A.Brown,1,2D.Bazin,1,2K.W.Brown,1,3R.J.Charity,4P.Farris,1,2A.M.Hill,1,2J.Li,1B.Longfellow,1,2,D.Rhodes,1,2,yW.Reviol,5andJ.A.Tostevin61FacilityforRareIsotopeBeams,MichiganStat...

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Exploiting dissipative reactions to perform in-beam -ray spectroscopy of the neutron-decient isotopes3839Ca A. Gade1 2D. Weisshaar1B. A. Brown1 2D. Bazin1 2K. W. Brown1 3R. J. Charity4P..pdf

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Exploiting dissipative reactions to perform in-beam -ray spectroscopy of the neutron-decient isotopes3839Ca A. Gade1 2D. Weisshaar1B. A. Brown1 2D. Bazin1 2K. W. Brown1 3R. J. Charity4P.

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