Spectroscopy of $^{26}$F to probe proton-neutron forces close to the drip line

0.4 MB·English

by  A. Lepailleur

Spectroscopy of 26F to probe proton-neutron forces close to the drip line
A. Lepailleur,1 O. Sorlin,1 L. Caceres,1 B. Bastin,1 C. Borcea,2 R. Borcea,2 B. A. Brown,3 L. Gaudefroy,4 S.
Gr´evy,5 G. F. Grinyer,1 G. Hagen,6,7 M. Hjorth-Jensen,3,8 G. R. Jansen,6,7 O. Llidoo,1 F. Negoita,2 F. de
Oliveira,1 M.-G. Porquet,9 F. Rotaru,2 M.-G. Saint-Laurent,1 D. Sohler,10 M. Stanoiu,2 and J.C. Thomas1
1Grand Acc´el´erateur National d’Ions Lourds (GANIL),
CEA/DSM - CNRS/IN2P3, B. P. 55027, F-14076 Caen Cedex 5, France
2IFIN-HH, P. O. Box MG-6, 76900 Bucharest-Magurele, Romania
3National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA
4CEA, DAM, DIF, F-91297 Arpajon, France
5Centre d‘E´tudes Nucl´eaires de Bordeaux Gradignan-UMR 5797, CNRS/IN2P3,
Universit´e de Bordeaux 1, Chemin du Solarium, BP 120, 33175 Gradignan, France
3 6Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
1 7Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA
0 8Department of Physics and Center of Mathematics for Applications, University of Oslo, N-0316 Oslo, Norway
2 9CSNSM, CNRS/IN2P3 - Universit´e Paris-Sud, F-91405 Orsay, France
n 10Institute of Nuclear Research of the Hungarian Academy of Sciences, P.O. Box 51, Debrecen, H-4001, Hungary
a
J A long-lived Jπ = 4+1 isomer, T1/2 = 2.2(1)ms, has been discovered at 643.4(1) keV in the
weakly-bound 26F nucleus. It was populated at GANIL in the fragmentation of a 36S beam. It
4 9
decays by an internal transition to the Jπ = 1+ ground state (82(14)%), by β-decay to 26Ne, or
2 1
beta-delayed neutron emission to 25Ne. From the beta-decay studies of the Jπ =1+1 and Jπ =4+1
] states,newexcitedstateshavebeendiscoveredin25,26Ne. Gatheringthemeasuredbindingenergies
x of the Jπ =1+−4+ multiplet in 26F, we find that the proton-neutron π0d ν0d effective force
1 1 9 5/2 3/2
e used in shell-model calculations should be reduced to properly account for the weak binding of
- 26F. Microscopic coupled cluster theory calculations using interactions derived from chiral effective
l 9
c field theory are in very good agreement with the energy of the low-lying 1+,2+,4+ states in 26F.
1 1 1
u
Including three-body forces and coupling to the continuum effects improve the agreement between
n
experiment and theory as compared to theuse of two-body forces only.
[

1 PACSnumbers: 21.10.Dr,21.60.Cs,21.60.De,23.35.+g,23.20.Lv
v
3
0 Introduction.- Understanding the boundaries of the body proton-neutron and neutron-neutron interactions,
8 nuclearlandscapeandtheoriginofmagicnucleithrough- the coupling to the continuum [13] effects and the three
5 out the chart of nuclides are overarching aims and intel- body forces [14, 15].
1. lectual challenges in nuclear physics research [1]. These Thestudyof26F,whichisboundbyonly0.80(12)MeV
0 are major motivations that drive the developments of [16], offers a unique opportunity to investigate several
3 present and planned rare-isotope facilities. Studying the aspects of the nuclear force. The 26F nucleus can be
1 evolutionofbindingenergiesforthe groundandfirstfew modeled using a simplified single-particle (s.p.) descrip-
v: excitedstatesinatomicnucleifromthevalleyofstability tion as a closed 24O core plus a deeply bound proton in
Xi to the drip line (where the next isotope is unbound with the π0d5/2 orbital (Sπ(25F)≃ -15.1(3) MeV [17]) plus
respect to the previous one) is essential to achieve these an unbound neutron (S (25O)≃ 770+20 keV [7]) in the
ν −10
ar endeavours. Understanding these trends and providing ν0d3/2 orbital. This simplified picture arises from the
reliable predictions for nuclei that cannot be accessed fact that the first excited state in 24O lies at 4.47 MeV
experimentally require a detailed understanding of the [4, 6] and the π0d and ν0d single particle energies
5/2 3/2
properties of the nuclear force [2, 3]. arewellseparatedfromtheotherorbitals. Thelow-lying
Intheoxygenisotopes,recentexperimentshaveshown Jπ = 1+,2+,3+,4+ states in 26F thus arise, to a first
1 1 1 1
that the drip line occurs at the doubly magic 24O16 [4– approximation, from the interactions of nucleons in the
6], as 25,26O are unbound [7, 8]. The role of tensor and π0d and ν0d orbits.
5/2 3/2
three-body forces was emphasized in [9, 10] to account
for the emergence of the N = 16 gap at 24O and the Present experimental knowledge concerning the mem-
16
’early’appearanceofthedriplineintheOisotopicchain, bers of the Jπ =1+,2+,3+,4+ multiplet in 26F is as fol-
1 1 1 1
respectively. On the other hand, with the exception of lows. A Jπ = 1+ assignment has been proposed in [18]
1
28F [11] and 30F which are unbound, six more neutrons for the ground state of 26F from the observationthat its
can be added in the F isotopic chain before reaching the beta decay proceeds to the Jπ = 0+, Jπ = 2+ states
1 1
drip line at 31F [12]. One can therefore speculate that and a tentative Jπ = 0+ state in 26Ne. The half-life
22 2
the extension of the drip line between the oxygen and of 26F was found to be 10.2±1.4 ms with a P value of
n
fluorine, as well as the odd-even binding of the fluorine 11±4% [18]. A mass excess ∆M of 18.680(80)MeV was
isotopes, arise from a delicate balance between the two- determined for 26F in [16] using the time-of-flight tech-
2
nique. The Jπ = 2+ state was discovered at 657(7) keV
1
[19] from the fragmentation of 27,28Na nuclei. In addi-
tion a charge-exchange reaction with a 26Ne beam was
used in [20] to study unbound states in 26F. In this re-
action,a neutroncapture to the νd orbitalanda pro-
3/2
ton removal from the πd (which are both valence or-
5/2
bitals) are likely to occur leading to the Jπ = 1+ −4+
1 1
states. The resonance observed at 271(37) keV above
the neutron emission threshold [20] could tentatively be
attributed to the Jπ = 3+ in 26F, as it was the only
1
state of the Jπ =1+−4+ whichwas predictedto be un-
1 1
bound. With the determination of the binding energies
ofthe Jπ =1+−3+ states,the only missinginformation
1 1
is the energy of the Jπ = 4+ state. In this Letter, we
1
demonstrate that the 4+ state is isomeric and decays by
1
competing internal transition and β decay. Its binding
energyis determined andthose of the 1+−2+ states are
1 1
re-evaluated. The comparison of the measured binding
energies of the Jπ =1+1 −4+1 states with two theoretical FIG.1: (Coloronline)(a): γ-rayspectraobtainedupto2ms
approaches, the nuclear shell model and Coupled Clus- after the implantation of 26F (upper spectrum), or after the
ter (CC) theory, provides a stringent test of the nuclear implantation of any nucleus except 26F (middle spectrum).
forces, where a large proton-to-neutron binding energy Thebottomspectrumshowstheβ-gatedγ-raysfollowingthe
asymmetry is present. implantationof26F.(b)Timespectrabetweenimplanted26F
andγ-rays,fromwhichhalf-liveswerededuced. The643.4(1)
Experiment.- The 26F nuclei were produced through keV and 4+ →2+ (1499.1(4) keV) transitions have thesame
thefragmentationofa77.6MeV/A36S16+primarybeam half-life,whileth1eonegatedonthe2+ →2+ (1672.5(3) keV)
with a mean intensity of 2 µAe in a 237mg/cm2 Be tar- transition has a larger half-life. (c): 2β-gate1d γ-ray spectrum
get. They were selected by the LISE [21] spectrometer following the implantation of 26F up to 30 ms. Symbols and
at GANIL, in which a wedge-shaped degrader of 1066 colors indicate which lines correspond to the β-decay of the
µm was inserted at the intermediate focal plane. The 1+ ((cid:7),black) and 4+ ((cid:4), red) or to the β delayed-neutron
produced nuclei were identified from their energy loss in branch(N,blue). Thesamecolorcodesareusedinthedecay
a stack of Si detectors and by their time-of-flight with schemeofFig. 2. Twolines(∗,green) couldnotbeplacedin
thedecay scheme of 26F.
respect to the GANIL cyclotron radio frequency. The
production rate of 26F was 6 pps with a purity of 22%
and a momentum acceptance of 2%. Other transmitted
nuclei, ranked by decreasing order of production, were γ-rays are detected in coincidence with a β transition.
28Ne, 29Na, 27Ne, 24O, 22N and 30Na. They were im- As the 643.4(1) keV is not in coincidence with β par-
planted in a 1 mm-thick double-sided Si stripped detec- ticles it must correspond to an internal transition (IT)
tor (DSSSD) composed of 256 pixels (16 strips in the X de-excitinganisomeric state in26F,whichhas a half-life
and Y directions) of 3×3 mm2-each located at the final of 2.2(1) ms (see Fig. 1(b)). This isomer is likely the 4+
focal point of LISE. This detector was used to detect state we are searching for. It either decays directly to
the β-particles in strips i,i±1 following the implanta- the 1+ ground state, hereby establishing the 4+ state at
tion of a radioactive nucleus in a given pixel i. With an 643.4(1)keV.Alternatively,the643.4(1)keVenergymay
energy threshold of ∼80 keV in the individual strips, a correspond, but with a weak level of confidence, to the
β-efficiencyof64(2)%wasachievedfor26Fwhichwasim- 657(7)keVstateobservedin[19]. Inthishypothesis,the
planted at central depth of the DSSSD. The β-efficiency isomerism of the 4+ state would be due to the emission
has been determined from the comparison of the inten- ofaverylowenergy4+ →2+ transition(upto10keVto
sity of a given γ-ray belonging to the decay of 26F gated ensure having a long-lived isomer), then followed by the
or not on a β-ray. Four clover Ge detectors of the EX- 2+ →1+ transition. Ineithercase,theexcitationenergy
OGAM array [22] surrounded the DSSSD to detect the of the 4+ state lies at approximately 650(10) keV.
γ-rays,leading to a γ-ray efficiency of 6.5% at 1 MeV. The decay of this 4+ state occurs through a competi-
The γ-ray spectra obtained up to 2 ms after the im- tion between an internal transition (IT) and β-decay to
plantationofaradioactivenucleusareshowninFig.1(a). two states in 26Ne. The half-lives corresponding to the
Inthisframetheupper(middle)spectrumisobtainedby IT (2.2(1)ms)aswellastothe1499.1(4)keV(2.4(2)ms)
requiringthat26F(allexcept26F)precedesthedetection and 1843.4(8) keV (2(1)ms) peaks of Fig. 1(c) are the
of a γ ray. A delayed γ-ray transition at 643.4(1) keV is same. These two transitions are seen in mutual coin-
clearly observed after the implantation of 26F. The bot- cidences, as well as with the 2017.6(3) keV γ-ray, pre-
tomspectrumofFig.1(a)isoperatedinsimilarcondition viously assigned to the 2+ → 0+ transition in 26Ne in
1 1
than the top one, with the additional requirement that [18]. This establishes two levels at 3516.7(4) keV and
3
FIG. 3: (Color online) Calculated and experimental interac-
tion energies Int(1−4) in MeV in 26F. Shell-model calcula-
tionsareshowninthefirstcolumnusingtheUSDAorUSDB
interactions, while the third column shows results obtained
withCCcalculations. Experimentalresultsareinthecenter.
The thicknessof thelines corresponds to ±1σ error bar.
sition coefficient IT. These parameters are furthermore
constrainedbytheamountofthe643.4(1)keVγ-raysob-
FIG. 2: (Color on line) Decay scheme obtained from the de- servedper implanted 26F nucleus,leading to R= 42(8)%
caysofthe4+ (red)and1+ states(black)in26Fto26Neand and IT=82(11)%.
25Ne(blue). ShellmodelpredictionsobtainedwiththeUSDB
The β feedings derived from the observed γ-ray in-
interaction are shown in theright hand side.
tensities are given in Fig. 2. In the β-delayed neutron
branchof26Fto25Ne,somelevelsobservedin[18,25,26]
areconfirmed,whileanewstateisproposedat3114.1(8)
5360.1(9) keV in 26Ne as shown in Fig. 2. Following keV as the 1413.2(7) keV and 1700.9(4) keV γ-rays are
the Gamow-Teller β-decay selection rules the 4+ isomer in coincidence and the summed γ-ray energy is observed
shouldmainlyproceedtotheJπ =4+ stateinthevibra- at 3116(2) keV. A P value of 16(4)% (consistent with
1 n
tor nucleus 26, which we attribute to the 3516.7(4) keV P =11(4)% [18]) is extracted for 26F from the observa-
n
state. tion of the 979.7 keV γ-ray in the grand-daughter nu-
All other observed transitions in Fig. 1(c) from 26F cleus 25Na whose branching ratio of 18.1(19)% was de-
belongto the decayofthe 1+ groundstate,astheir half- termined in [27]. We therefore adopt a mean value of
livesdiffersignificantlyfromthatofthe4+isomericstate. Pn=13.50(40)% for 26F. The proposed level scheme and
branchingratiosagreerelativelywellwiththeshell-model
Thetwoγ-raytransitionsat1672.5(3)keVand1797.1(4)
calculation shown on the right side of Fig. 2.
keV were found to be in coincidence with the 2017.6(3)
keV transition, but not in mutual coincidence. This es- Thediscoveryofthisnewisomerhasanimportantcon-
tablishes two levels at 3690.1(4) keV and 3814.7(5) keV sequence onthe determinationof the atomic massof the
whichhavecompatiblehalf-lives of7.7(2)ms,and7.8(5) 26Fgroundstateaswellontheinterpretationoftheone-
ms, respectively. These states presumably belong to the neutronknock-outcrosssectionsfrom26FofRef. [28]. It
two-phonon multiplet of states Jπ = 0+,2+,4+ among is very likely that the measuredatomic mass ofRef. [16]
2 2 1
which the 3516.7(4) keV one was assigned to Jπ = 4+ correspondsto a mixture of the groundand the isomeric
1
(see above). Using in-beam γ-ray spectroscopy from the states (unknown at that time). As the 26F nuclei were
fragmentation of a 36S beam [23], the feeding of the produced in the present work and that of [16] in similar
3516.7(4)keVlevelwasthe largest,thatofthe 3689.8(4) fragmentation reactions involving a large number of re-
keV state was weaker, while the state at 3814.7(5) keV moved nucleons, we can reasonably assume that the 26F
was not fed. As this method mainly produces Yrast isomeric ratio is the same in the two experiments. The
states, i.e. states having the highest spin value in a shiftinthe26Fatomicmassasafunctionoftheisomeric
given excitation energy range, we ascribe Jπ = 2+ to ratio R amounts to -6.43 keV/%, which for R=42(8)%
2
the state at 3690.1(4) keV, in accordance with [24], and yields -270(50) keV.
Jπ =0+ to the stateat3814.7(5)keV.The fitting ofthe Discussion.- The comparisonbetweenthe experimen-
2
decay half-lives must include the direct 1+ decay of 26F talbindingenergiesofthesestatescannowbemadewith
1
as well as the partial feeding from the 4+ → 1+ tran- two theoretical approaches, the nuclear shell model and
1 1
sitions. This leads to a growth at the beginning of the CC theory. The experimental (calculated) interactions
time spectrum (Fig. 1 (b) for the 1673 keV γ-ray)which elements arising from the coupling between a d pro-
5/2
dependsontheisomericratioRandontheinternaltran- tonandad neutron,labeledInt(J),areextractedfrom
3/2
4
the experimental (calculated) binding energies BE as the Fermi sphere with a Fermi momentum k in sym-
F
metric nuclear matter [38]. The parameters recently es-
Int(J)=BE(26F)J−BE(26Ffree). tablished in the oxygen chain [15] are adopted in the
present work. We use a Hartree-Fock basis built from
In this expression BE(26F ) corresponds to the bind-
free N = 17 major spherical oscillator shells with the os-
ing energy of the 24O+1p+1n system, in which the va- max
cillatorfrequency~ω =24MeV.Thisissufficientlylarge
lenceprotoninthed orbitandtheneutroninthed
5/2 3/2 toachieveconvergenceofthe calculationsforallisotopes
orbit do not interact. It can be written as
considered. Using two-body nucleon-nucleon forces we
BE(26F )=BE(25F) +BE(25O) −BE(24O) . gettheground-stateenergyof26Fat−173.2MeVwhich
free 5/2+ 3/2+ 0+ is underbound by ∼ 11 MeV compared to experiment.
Using the relative binding energy of +0.77+20 MeV However,therelativespectrafortheexcitedstatesarein
−10
fair agreement with experiment (see Fig. 3). In order to
[7] between 24O and 25O , the measured atomic masses
accountforthecouplingtothecontinuumin26F,weusea
in 25F and 26F [16], and the shift in energy due to the
realWoods-Saxonbasisfortheν1s andν0d partial
isomeric content (see above) it is found that the exper- 1/2 3/2
waves[39]. Theinclusionofcontinuumeffectsandthree-
imental value of Int(1) is -1.85(13) MeV. The values of
nucleon forces improve the situation, the ground state
Int(2)= -1.19(14) MeV and Int(4)=-1.21(13) MeV are
obtained using the Jπ = 2+ and Jπ = 4+ energies of energy is at -177.07 MeV, and the low-lying spectra is
1 1 in very good agreement with experiment. The Jπ = 3+
657(7)keV and 643.4(1) keV, respectively. A value of
state in 26F is a resonance and to compute this state we
Int(3)=-0.49(4) MeV is derived from the energy of the
Jπ =3+ resonancewithrespectto the 25F groundstate. needaGamow-Hartree-Fockbasis[40]. Wearecurrently
1 workingongeneralizingthetwo-particleattachedCCim-
In the shell-model calculations of Refs. [29, 30], the
plementation to a complex basis. Therefore, the interac-
two-body matrix elements corresponding to interactions
tion energy of the J = 3 state is not shown in Fig. 3.
inthe sdvalence spacearefittedto reproduceproperties
Consistently with the shell-model calculations described
ofknownnuclei. Applyingtheseinteractionstonucleinot
above,asimplepictureemergesfromthemicroscopicCC
included in the global fits (such as bound and unbound
calculations: about 85% of the 1+ −4+ wave functions
states in 26F) implies that shell-model calculations to-
are composed of 1s0d-shellcomponents, in which config-
wards the drip lines can be viewed as predictions. Due
urations consisting of the π0d and ν0d s.p. states
tothe strongcouplingtothe continuum,andalikelyab- 5/2 3/2
play a major role.
sence of many-body correlationsnot included in the fits,
Conclusions.- To summarize, a new Jπ = 4+ isomer
these interactions may fail in reproducing properties of 1
nuclei like 26F. Owing to its simple structure, 26F pro- witha2.2(1)ms half-life hasbeendiscoveredat643.4(1)
keV. Its isomeric decay to the Jπ = 1+ ground state
vides a unique possibility to probe the strength of the 1
and β-decay to the Jπ = 4+ state in 26Ne were ob-
proton-neutron interaction close to the drip line. The 1
wavefunctions of the Jπ =1+−4+ states are composed served. Gathering the β-decay branches observed from
of mainly (80−90%) pure π10d 1⊗ν0d component. the Jπ = 1+1 and Jπ = 4+1 states, partial level schemes
5/2 3/2 of 26Ne and 25Ne were obtained. In addition, the 26F
BycalculatingallstatesintheJπ =1+−4+ multiplet,it
1 1 nucleusisabenchmarkcaseforstudying proton-neutron
canbeseeninFig. 3thattheJπ =1+stateislessbound
1 interactions far from stability. The experimental states
than calculated by about 17% (8%) and that the multi-
J = 1+ − 4+ arising from the πd ⊗ νd coupling
plet of experimental states is compressed by about 25% 5/2 3/2
in 26F are more compressed than the USDA and USDB
(15%) compared with the USDA (USDB) calculations. 9
shell model results. The experimental Jπ = 1+,2+,4+
This points to a weakening of the residual interactions, 1 1 1
states are less bound as well. These two effects point to
which caused the energy splitting between the members
a dependence of the effective two-body interaction used
of the multiplet.
in the shellmodel as a function ofthe proton-to-neutron
We have also performed microscopic CC [31, 32] cal-
binding energy asymmetry. Coupled-cluster calculations
culations for 26F. This method is particularly suited for
including three-body forces and coupling to the particle
nuclei with closed (sub-)shells, and their nearest neigh-
continuum are in excellent agreement with experiment
bors. Moreover, CC theory can easily handle nuclei in
for the bound low-lying states in 26F.
which protons and neutrons have significantly different
binding energies. To estimate the π0d − ν0d in-
5/2 3/2
teraction energy (Int(J)), we use CC theory with singles
and doubles excitations with perturbative triples correc- Acknowledgments
tions[33,34]fortheclosed-shellnucleus24O,theparticle-
attached CC method for 25O and 25F [35] and the two- This work was partly supported by the Office of Nuclear
particle attached formalism for 26F [36]. We employ in- Physics, U.S. Department of Energy (Oak Ridge National
teractions from chiral effective field theory [37]. The ef- Laboratory), the NSF grant PHY-1068217, the OTKA con-
fects of three-nucleon forces are included as corrections tractK100835,thegrantoftheRomanianNationalAuthority
tothenucleon-nucleoninteractionbyintegratingonenu- for Scientific Research, CNCS UEFISCDI, PN-II-RU-TE-
cleon in the leading-orderchiral three-nucleonforce over 2011-3-0051 as well as by FUSTIPEN (French-U.S. Theory
5
Institute for Physics with Exotic Nuclei) under DOE grant andtheNoturprojectinNorway. TheCENBGisgreatlyac-
number DE-FG02-10ER41700. This research used compu- knowledgedfortheloanoftheDSSSDdetector. A.L.thanks
tational resources of the National Center for Computational V.Tripathiforcommunicatinginformationwhichweusedfor
Sciences, the National Institute for Computational Sciences, calibration purposes.
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