Intermediate-energy inverse-kinematics one-proton pickup reactions on neutron-deficient $fp$-shell nuclei

0.67 MB·English

by  S. McDaniel

Intermediate-energy inverse-kinematics one-proton pickup reactions on
neutron-deficient fp-shell nuclei
S. McDaniel,1,2 A. Gade,1,2 J.A. Tostevin,3 T. Baugher,1,2 D. Bazin,1 B.A. Brown,1,2 J.
M. Cook,1,2 T. Glasmacher,1,2 G. F. Grinyer,1,∗ A. Ratkiewicz,1,2 and D. Weisshaar1
1National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824
2Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824
3Department of Physics, Faculty of Engineering and Physical Sciences,
University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom
(Dated: January 16, 2012)
Background: Thick-target-inducednucleon-addingtransferreactionsontoenergeticrare-isotope
beamsareanemergingspectroscopictool. Theirsensitivitytosingle-particlestructurecomplements
one-nucleonremovalreactioncapabilitiesinthequesttorevealtheevolutionofnuclearshellstruc-
tureinveryexoticnuclei. Purpose: Toaddintermediate-energy,carbon-target-inducedone-proton
2 pickupreactionstothearsenalofγ-raytaggeddirectreactionsapplicableintheregimeoflowbeam
1 intensities and to apply these for the first time to fp-shell nuclei. Methods: Inclusive and partial
0 crosssectionsweremeasuredforthe12C(48Cr,49Mn+γ)Xand12C(50Fe,51Co+γ)Xprotonpickup
2 reactions at 56.7 and 61.2 MeV/nucleon, respectively, using coincident particle-γ spectroscopy at
n the NSCL. The results are compared to reaction theory calculations using fp-shell-model nuclear
a structure input. For comparison with our previous work, the same reactions were measured on
J 9Be targets. Results: The measured partial cross sections confirm the specific population pattern
3 predictedbytheory,withpickupintohigh-(cid:96)orbitalsbeingstronglyfavored;drivenbylinearandan-
1 gular momentum matching. Conclusion: Carbon target-induced pickup reactions are well-suited,
in the regime of modest beam intensity, to study the evolution of nuclear structure, with specific

] sensitivities that are well described by theory.
x
e
l- I. INTRODUCTION est beam intensities of 1 − 103 particles/second, lumi-
c nosities comparable to stable-beam experiments can be
u
restored by employing thick reaction targets and using
n For several decades, direct reactions have been cru-
in-beam γ-ray spectroscopy to tag the final states of the
[ cialtoolsfortheinvestigationofthesingle-particlestruc-
projectile-likereactionresidues[1]. Overthepastdecade,
tures that underlie the complex many-body problem of
2 γ-ray tagged, thick 9Be target-induced one- and two-
theatomicnucleus. Atsufficientlyhighcollisionenergies
v
nucleon knockout reactions in inverse kinematics, such
3 one or two nucleons can be removed from the projectile
as9Be(AZ,A−1Z+γ)Xand9Be(AZ,A−2(Z−2)+γ)X,have
0 ortransferredbetweenthetargetandprojectilenucleiin
4 their fast, surface-grazing collisions. Classic examples of been developed as spectroscopic reaction tools. In the
2 such spectroscopic direct reactions are light-ion-induced low intensity, fast secondary beam regime these reaction
. mechanisms can probe in some detail the single-particle
1 one- and two-nucleon transfer reactions on thin, stable
content of the nuclear many-body wave function at and
0 targets at incident energies of several MeV per nucleon.
2 Examples are the (d,p), (p,d), (p,t) and (t,p) reactions. near the Fermi surface(s) [2].
1 Here, it is the detection of the light charged particles in In these reactions, one-nucleon removal selectively
:
v the exit channel that allows the determination of final- populateshole-likeconfigurationswithrespecttothepro-
i state energies, cross sections and their angular distribu- jectile ground state. Similar to transfer reactions, they
X
tions, having sensitivity to the location, spectroscopic probe the location of such single-hole states, their spec-
r strengths and the transferred orbital angular momenta troscopic strengths and orbital angular momenta. Sud-
a
of the active one- and two-nucleon configurations (over- den two-proton (neutron) removal reactions from neu-
laps), respectively. tron(proton)-richnucleialsoproceedasdirectreactions.
With the advent of rare-isotope beam facilities, short- They probe, specifically, the parentage and phase of the
lived neutron-rich or neutron-deficient nuclear species participating two-nucleon configurations near the well-
have become available for nuclear structure studies. boundFermisurfaceofthegroundstateoftheprojectile,
Many of the most exotic nuclei can be produced ef- built upon the final states of the projectile-like reaction
ficiently by projectile fragmentation and are available residues[3–6]. Detailsofthisnuclearstructuremodelin-
for experiments as fast heavy-ion beams with v/c ≥ formationiscarriedbythetwo-nucleonamplitudes(over-
0.30. In this regime, of very exotic nuclei with mod- laps), see e.g. [4].
Tocomplementthisarsenaloffast-beam,inversekine-
matics nucleon removal reactions, one-nucleon pickup
reactions onto fast projectile beams from thick car-
∗ Present address GANIL, CEA/DSM-CNRS/IN2P3, Bvd Henri bon and beryllium targets have recently been stud-
Becquerel,14076Caen,France ied as a spectroscopic probe sensitive to particle-like
2
states/configurations [7–9]. The choice of reaction tar- fragmentseparator[12]. AnachromaticAlwedgeof300-
get is now motivated by generic linear and angular mo- mg/cm2thicknesstogetherwithslitsystemswereusedto
mentum matching considerations and that, at high col- optimizethebeampurityon50Fe. Theresultingcocktail
lision energies, the pickup of well-bound target nucleons beamofN =24isotoneswastransmittedtothereaction
is favored [10, 11]. In common with the thick-target nu- target position of the S800 spectrograph at typical rates
cleon removal experiments, the energy resolution of the of 2500, 2000, and 500 particles per second and purities
populated final-states relies on γ-ray spectroscopy per- of 39%, 40%, and 11%, respectively, for 48Cr, 49Mn, and
formed in coincidence with the detection of the heavy 50Fe at ∆p/p=1% total A1900 momentum acceptance.
projectile-like pickup reaction residues. However, unlike Reaction targets of 72.8(13)-mg/cm2 thick 12C and
in removal reactions, and rooted in the two-body nature 188(4)-mg/cm2thick9Bewereusedatthetargetposition
of the reaction mechanism, the longitudinal momentum of the S800 spectrograph [13] for the different settings.
distributionoftheprojectile-likereactionresiduescarries Thehigh-resolutionγ-raydetectionsystemSeGA[14],an
no useful information on the orbital angular momentum arrayof32-foldsegmentedhigh-puritygermaniumdetec-
of the transferred nucleon. Rather, it can be used to es- tors, was used to detect the de-excitation γ rays emitted
timate whether there are significant non-two-body final- by the reaction residues. Sixteen of the SeGA detectors
state contributions to the measured reaction yields [9]. were arranged in two rings with relative angles of 90◦ (9
So far, thick 12C and 9Be targets were employed and detectors)and37◦ (7detectors)withrespecttothebeam
compared [9] for the fast one-neutron pickup studies. axis. The high degree of segmentation allows for event-
Only 9Be targets have been used to date for measured by-eventDopplerreconstructionoftheγ raysemittedby
one-proton pickup cases [7, 8]. The goals of the present theprojectile-likereactionresiduesinflight. Theangleof
work are two-fold. We investigate: theγ-rayemissionthatenterstheDopplerreconstruction
(i) the use of a 12C target to induce the fast-beam one- is deduced from the position of the segment that regis-
proton pickup reaction of type 12C(AZ,A+1(Z+1)+γ), teredthelargestγ-rayenergydeposition. Thephotopeak
includingthemeasurementandtheoreticaldescriptionof efficiency of the detector array was calibrated with stan-
partial cross sections, and dard sources and corrected for the Lorentz boost of the
γ-ray distribution emitted by the projectile-like reaction
(ii) extension of the study of this spectroscopic tool into
residues in flight at v/c>0.25.
fp-shell systems.
Animportantaspectoftheuseofpickupontofastpro-
jectilebeamsistheanticipatedselectivityofthistransfer
49Mn
process to high-(cid:96) orbitals, or fragments thereof, in the s)
projectileresidues,promisingthistechniqueassuitedfor nit
u 48Cr
identifying intruder states that are direct indicators of b. 10
shell evolution. This makes projectiles with vacancies in ar 47Cr
the proton 1f7/2 and 2p3/2,1/2 orbits a logical choice to oss ( 46V
advance such one-proton pickup developments, to high- y l
light and contrast the pickup yields into these (cid:96)=3 and erg
(cid:96)=1 single-proton configurations. n
E
For the present study we use a cocktail beam of
projectiles containing the N=24 isotones 48Cr and
50Fe. We will focus on the 12C(48Cr,49Mn+γ)X and 1
Time-of-flight (arb. units)
12C(50Fe,51Co+γ)X reactions at mid-target energies of
56.7 and 61.2 MeV/nucleon, respectively. To allow com-
parisonwiththeearlierwork(thatused9Betargets)the
FIG.1. (Coloronline)Particleidentificationforthereaction
9Be(48Cr,49Mn+γ)X and 9Be(50Fe,51Co+γ)X reactions,
residues in the 9Be(48Cr,49Mn)X setting. Plotted is the en-
at mid-target energies of 50.7 and 54.8 MeV/nucleon,
ergy loss measured with the S800 ionization chamber versus
respectively, were also measured with the same experi-
the time of flight measured between the plastic trigger scin-
mental setup. tillator at the back of the S800 focal plane and a scintillator
at the spectrograph’s object location.
II. EXPERIMENTS Reaction residues were identified event-by-event with
thefocal-planedetectionsystem[15]oftheS800spectro-
Theprojectilebeamcontaining48Crand50Fewaspro- graph. The energy loss measured in the S800 ionization
duced by fragmentation of a 160-MeV per nucleon 58Ni chamber and flight times, corrected for the angle and
primary beam provided by the Coupled Cyclotron Fa- momentum of each nucleus, were used to identify the
cility at the National Superconducting Cyclotron Lab- projectile-like reaction residues exiting the target. The
oratory (NSCL) at Michigan State University. The incoming projectiles were identified from their difference
893 mg/cm2 thick 9Be production target was located in flight time measured with two plastic scintillators up-
at the mid-acceptance target position of NSCL’s A1900 stream of the target. The particle-identification spec-
3
trumfor49Mnproducedin48Cr+12CisshowninFig.1. [17].
Theprojectilebeamspassingthroughthetargetareclose The single-particle cross sections (computed for a pro-
in magnetic rigidity to the respective one-proton pickup ton+projectilespectroscopicfactorofone)andtheshell-
residues and the beam blocker located at the entrance of model spectroscopic factors enter the calculation of the
theS800focalplanehadtobeusedtoblockalargefrac- theoretical (angle integrated) pickup cross sections that
tion of the unreacted projectiles. Still, the most intense are compared to the experimental results. For each final
contribution in the identification spectrum in Fig. 1 is state, Jπ, of the projectile-like residue the theoretical
from unreacted 48Cr. cross section is
Foreachtargetandprojectilebeam,theinclusivecross
sections for the one-proton pickup reaction to all projec- (cid:18) A (cid:19)N
σ (Jπ)= p S (Jπ)σ (Jπ) . (1)
tile + proton bound final states were deduced from the th A +1 SM sp
p
yield of detected pickup residues divided by the num-
ber of incoming projectiles relative to the number den- The first factor, that depends on the projectile mass
sity of the 9Be and 12C reaction targets, respectively. A and the principal harmonic oscillator quantum num-
p
The deduced inclusive cross sections are σinc(49Mn) = ber, N, of the transferred proton orbit, is a small (near
exp
2.00(13) mb and σinc(51Co) = 0.53(13) mb for the unity) center-of-mass correction to the shell-model spec-
exp
12C-induced pickups and σinc(49Mn) = 1.63(8) mb and troscopic factors, SSM. N=3 for the present proton fp-
exp
shell cases. The measured cross sections and the calcu-
σinc(51Co) = 0.57(8) mb for the 9Be-induced pickups.
exp lated (single-particle) cross sections σ (Jπ) to specific
Thequoteduncertaintiescombinestatisticalandsystem- sp
final states in 49Mn and 51Co are both inclusive with
aticerrors, includingthestabilityofthesecondarybeam
respect to the final states of the target residues. The
composition,thechoiceofthesoftwaregates,andcorrec-
calculations thus include contributions from transitions
tions for the acceptance losses in the tails of the residue
involving several 11B and 8Li final states. These will be
parallel momentum distributions.
detailed in the following subsections for the 12C and 9Be
Event-by-event in-beam γ-ray spectroscopy in coinci-
target cases.
dence with detection of the projectile-like pickup residue
The spectroscopic amplitudes of the proton + projec-
allowedtheidentificationofexcitedfinalstatesandmea-
surement of their population in the pickup to 49Mn. No tileboundstateoverlaps,[48Cr(0+)⊗n(cid:96)j]and[50Fe(0+)⊗
bound excited states were observed for 51Co, for which n(cid:96)j], were taken from fp-shell-model calculations using
the GXPF1A effective interaction [18]. The associated
a proton separation energy of only S ≈ 90 keV is pre-
p
proton + projectile bound state wave functions (radial
dicted from systematics [16].
overlaps) were calculated in real Woods-Saxon potential
Partial cross sections to individual final states were
wells with diffuseness parameter a = 0.7 fm and spin-
obtained from the efficiency-corrected full-energy peak 0
orbit interaction strength of 6 MeV. The reduced radius
areasintheDopplerreconstructedγ-rayspectrarelative
parameters, r , of these potentials were adjusted to re-
tothenumberofpickupproducts,andwerecorrectedfor 0
producetherootmeansquared(rms)radiiofeachproton
feeding. Unfortunately, the statistics were not sufficient
totagthefinalstateofthe11Band8Litargetresiduesin single-particleorbitalgivenbysphericalHartreeFockcal-
culations, as has been discussed in detail elsewhere [19].
the laboratory-frame γ-ray spectra (see [7] for a higher
These same Hartree-Fock (HF) calculations were used
statisticssd-shellcaseforwhichitwaspossibletotagthe
8Li target residues left in the first excited state). to calculate the projectile and projectile-residue densi-
ties, for calculation of the channel distorting potentials,
as will be discussed below. The r values were 1.24 and
0
1.25fmforthe1f and2p-shellprotonorbitalsin49Mn,
III. THEORETICAL REACTION MODEL 7/2
respectively, and 1.23 fm for the 1f proton orbital in
7/2
51Co.
The one-proton transfers, from 12C and 9Be, are as-
sumed to take place in a single step from the ground
states of these targets to bound proton single-particle
states built on the ground states of the projectiles. So, A. Reactions on 12C target
aswasusedinearlierwork,theone-protonpickupsingle-
particle cross sections are calculated using the post-form The proton is assumed to be transferred in a single
of the distorted waves Born approximation (DWBA) to step from a bound state in the 12C(g.s.) into a pro-
the pickup reaction transition amplitude. The transfer ton + projectile bound state. The 11B target residue
interaction (that binds the transferred proton and the is assumed to be left in one of three bound states, the
target residues 11B and 8Li) is treated in finite-range. 3/2− ground state, the 1/2− excited state at 2525 keV,
1 1
The calculations assume that both the entrance and exit and the 3/2− excited state at 5020 keV. The shell-model
2
channelsaretwo-bodyandhencethattheprotonistrans- spectroscopicfactors(WBPeffectiveinteraction[20])for
ferred to bound states in the projectile-like residue and these three states essentially exhaust the expected spec-
the target-like residues remain bound. All calculations troscopic strength, of 4, being 3.16, 0.58, and 0.19, re-
were performed using the direct reactions code fresco spectively. The residual strength, of 0.07, is distributed
4
over many states up to the proton separation energy of
TABLE I. Inputs used in the reaction model calculations for
11B and is neglected. Woods-Saxon potentials are used
12C(48Cr,49Mn)11B(Iπ). Shown are the 49Mn final-state an-
to generate these proton + 11B bound states, their ge-
gularmomentaandparities,Jπ,theirexcitationenergies,E ,
x
ometry taken from Ref. [21]. These have reduced radius
protonconfigurations,n(cid:96) ,andeffectiveprotonseparationen-
j
parameter r0 =1.310 fm and diffuseness a=0.55 fm. ergies,Sr.eff. The11Bfinal-statespinsandparities,Iπ,effec-
p
tive proton separation energies, St.eff, and the single-particle
Thenucleardistortinginteractionsinthe12C+projec- p
cross sections, σ , for each transition are also shown.
tile (entrance) and 11B + pickup residue (exit) channels sp
were calculated. We adopted the method used in earlier 49Mn Target 12C→11B
fast nucleon removal reaction studies [19], i.e. by dou- Jπ E n(cid:96) Sr.eff Iπ St.eff σ
x j p p sp
ble folding the point neutron and proton densities of the
(keV) (MeV) (MeV) (mb)
projectiles and residues, 48Cr, 49Mn and 50Fe, 51Co, and
7/2− 262 1f 1.823 3/2− 15.957 3.724
of 12C, 11B with an effective nucleon-nucleon (NN) in- 7/2
1/2− 18.082 0.238
teraction[4]. Fortheprojectile-likesystemsthedensities
were obtained from spherical Skyrme (SkX interaction) 3/2− 20.977 0.179
Hartree-Fock (HF) calculations [24]. The target-like sys- 1/2− 1703 2p1/2 0.382 3/2− 15.957 0.029
tems, 12C and 11B, were assumed to have Gaussian den- 1/2− 18.082 0.010
sity distributions with rms radii of 2.32 fm and 2.11 fm. 3/2− 20.977 0.001
3/2− 1741 2p 0.344 3/2− 15.957 0.103
The proton pickup reactions to 49Mn were thus com- 3/2
puted as 48Cr(12C,11B(Iπ))49Mn(Jπ) leading to the 1/2− 18.082 0.008
Iπ = 3/2−, 1/2−, and 3/2−, 11B final states. The first 3/2− 20.977 0.003
1 1 2
excited Jπ =7/2−, 1/2−, and 3/2− final states of 49Mn
were considered. Pickup to the 5/2− ground state of
49Mnisnegligibleduetotheverysmallshell-modelspec- TABLE II. As Table I but for 12C(50Fe,51Co)11B(Iπ).
troscopic factor, S = 0.002. For the (as yet unob-
SM
served) 1/2− and 3/2− excited states we used the level 51Co Target 12C→11B
energies of the corresponding states in the 49Cr mirror Jπ Ex n(cid:96)j Spr.eff Iπ Spt.eff σsp
system. The energy of the 7/2− state is known to be (keV) (MeV) (MeV) (mb)
1
262 keV. 7/2− 0 1f 0.090 3/2− 15.957 2.708
7/2
1/2− 18.082 0.165
Table I summarizes the inputs to the reaction cal-
culations. There, Sr.eff = S (49Mn)−E (49Mn) is the 3/2− 20.977 0.129
p p x
effectiveprotonseparationenergyfromtheprojectile-like
residue, St.eff =S (12C)+E (11B) that from the target.
p p x
The single-particle proton pickup cross section to each B. Reactions on 9Be
final state of 49Mn is then the sum of the cross sections
to the three 11B final states. As expected, based on the The theoretical description of the 9Be-target-induced
WBPshell-modelspectroscopicfactorsshownabove,the
one-protonpickupreactionsfollowsourearlierimplemen-
11Bgroundstatetransitiondominatesintheseindividual
tation,aswaspresentedin[7]. Inthisinstancetwobound
single-particlecrosssections,σ . Itisalreadyclearfrom
sp and one unbound final state are expected to be strongly
TableIthatourhighprojectilebeamenergystronglyfa- populated in the 8Li target residue and will be consid-
vors(cid:96)=3pickup,tothe1f7/2 protonstateof49Mn,over ered. These are the 2+ ground state, the 1+ excited
1
(cid:96)=1pickuptotheotherfinalstates. Thisisunderstood state at 980 keV, and the 3+ state at 2255(3) keV, the
1
intuitively by generic, semi-classical linear and angular latterjustabovethefirstneutronthresholdofS (8Li)=
n
momentum (mis)matching arguments, e.g. [22, 23]. 2032.62(12) keV [16]. The 9Be(3/2−) to 8Li(I+) radial
Pickup to the weakly-bound dripline nucleus 51Co overlaps and their associated spectroscopic amplitudes
wascomputedsimilarly,as50Fe(12C,11B(Iπ))51Co,lead- used the Variational Monte Carlo (VMC) calculations of
ing to the same 11B final states. Only pickup to the Wiringa et al. [25], as were discussed in Ref. [7].
51Co(7/2−) ground state was considered due to the low As for the 12C target, the nuclear distorting interac-
protonseparationenergyofS (51Co)=90keV[16]. The tions in the entrance and exit channels were obtained by
p
double folding the point neutron and proton HF densi-
calculations of the single-particle cross sections are sum-
ties of the projectiles and their residues and of 9Be and
marized in Table II.
8Li with an effective NN interaction [4]. Both 9Be and
Thesecalculatedpartialandsummedtheoreticalcross 8Li were assumed to have Gaussian density distributions
sections, including the shell model spectroscopic factors with an rms radius of 2.36 fm.
and the center-of-mass corrections, are summarized in The pickup reaction to 49Mn was computed as
Tables V and VI. These results will be discussed and 48Cr(9Be,8Li(Iπ))49Mn(Jπ) to the three final states of
compared to the experimental data in Section IV. 8Li outlined above. The excited Jπ = 7/2−, 1/2− and
1 1
5
A. Proton pickup to 49Mn
TABLE III. As Table I but for 9Be( 48Cr,49Mn)8Li(Iπ).
49Mn Target 9Be→8Li Neutrondeficient49Mniswell-suitedtofurtherbench-
Jπ E n(cid:96) Sr.eff Iπ St.eff σ mark the spectroscopic value of fast-beam one-proton
x j p p sp
pickup reactions. Having six neutrons less than the only
(keV) (MeV) (MeV) (mb)
stable Mn isotope, its low proton separation energy of
7/2− 262 1f 1.823 2+ 16.888 2.213
7/2 S = 2085(25) keV [16] limits the number of proton-
1+ 17.870 0.882 p
bound states and so minimizes the impact of possible
3+ 19.143 0.811
(unobserved) indirect feeding on the determination of
1/2− 1703 2p1/2 0.382 2+ 16.888 0.021 the partial cross sections from γ-ray spectroscopy. Fur-
1+ 17.870 0.014 thermore, the proton shell structure of 49Mn allows one
3+ 19.143 0.004 to examine the high-(cid:96) orbital selectivity of the pickup
3/2− 1741 2p 0.344 2+ 16.888 0.049 reaction, predicted to be strongly favored by momen-
3/2
1+ 17.870 0.020 tum matching at high projectile energy. The yrast level
scheme of 49Mn, discovered in 1970 [26], is known up
3+ 19.143 0.014
to high spin values from extensive studies in the 90’s fo-
cusedonisospinsymmetry[27,28]. Twolow-lyingstates,
dominatedbysingle-particleconfigurationsinvolvingthe
proton 2p and 2p orbits, are expected around 1700
TABLE IV. As Table I but for 9Be(50Fe, 51Co)8Li(Iπ). 1/2 3/2
and 1740 keV, respectively, from comparison to the mir-
51Co Target 9Be→8Li ror nucleus 49Cr [29], but have not yet been observed.
Jπ E n(cid:96) Sr.eff Iπ St.eff σ The most recent work on 49Mn employed β-delayed pro-
x j p p sp
ton decay from 49Fe to populate excited states in 49Mn
(keV) (MeV) (MeV) (mb)
[30].
7/2− 0 1f 0.090 2+ 16.888 1.625
7/2
The measured inclusive one-proton pickup reac-
1+ 17.870 0.640
tions cross sections on the 12C and 9Be targets
3+ 19.143 0.593
are σinc(49Mn) = 2.00(13) mb and σinc(49Mn) =
exp exp
1.63(8) mb, respectively. These are comparable in mag-
nitude to the earlier one-proton pickup cross section to
the sd-shell nucleus 21Na, with a 9Be target, for which
3/2− 49Mn final states were considered. The input pa-
1 σinc =1.85(12) mb [7].
rametersandcalculatedcrosssectionsaresummarizedin exp
Forthepartialcrosssections,bycombiningthesingle-
TableIII,withthesameentriesasexplainedintheprevi-
particle cross sections from the reaction model calcula-
ous subsection. In this case the spectroscopic strengths
tions (Section III) with the associated GXPF1A shell-
of the different 8Li final states (for values, see [7]) are
modelspectroscopicfactors,adistinctivepopulationpat-
more equal and the ground state transition is less domi-
ternispredictedfromtheinterplayofmomentummatch-
nant. As previously, the one-proton pickup cross section
ing and proton shell structure. As can be seen from Ta-
toaparticular49Mnfinalstateisthesumofthesesingle-
ble V, below the proton separation energy of 49Mn, only
particle cross sections for the three 8Li final states. The
the first excited 7/2− state is predicted to be populated
calculationsconfirmtheselectivityofpickuptothehigh-
with appreciable cross section. Although the spectro-
(cid:96) final-state configuration.
scopicfactorsforpickuptothepredicted1/2− and3/2−
The proton pickup to 51Co, computed as states (proton (cid:96) = 1, 2p and 2p configurations)
1/2 3/2
50Fe(9Be,8Li(Iπ))51Co(7/2−) was treated similarly. are comparable to S (f ), the single-particle cross
gs SM 7/2
The details of the calculations are summarized in sections for pickup to the (cid:96) = 1 configurations are sup-
Table IV. pressed by two orders of magnitude compared to those
for the (cid:96)=3 orbital, independently of the target.
Figure 2 (upper panel) shows the Doppler-
reconstructed in-beam γ-ray spectra detected in
coincidence with 49Mn, produced in one-proton pickup
IV. RESULTS AND DISCUSSION
fromthe12Ctarget(left)andthe9Betarget(right). The
only transition attributed to 49Mn is the de-excitation
Wenowdiscusstheexperimentalresultsfromthereac- γ-ray from the first 7/2− to the 5/2− ground state,
tions induced on the even-even 48Cr and 50Fe projectiles measured at E =261 keV. This confirms the population
in comparison to the calculations presented above. We pattern predicted by theory with almost all cross section
also analyze the longitudinal momentum distributions of resulting from the pickup to the (cid:96) = 3, 7/2− state
the 49Mn and 51Co pickup residues from the reactions at 262 keV excitation energy. Within the level of the
on the 12C target with emphasis on confirming the (as- statistics, there is no evidence for the decays of the
sumed) two-body nature of the reaction mechanism. 1/2− and 3/2− excited states that are predicted to
6
80
12C target 49Mn 9Be target 140 TABLEV.Shell-modelprotonconfigurations[48Cr(0+)⊗n(cid:96) ]
j
70 β = 0.317 β = 0.273 andtheirspectroscopicfactors,SSM,single-particlecrosssec-
120 tionstotheindividualfinalstatesin49Mn(summedoverthe
60 included 11B and 8Li final states), and the theoretical cross
100
V50 260.7(12) keV 260.8(11) keV sections σth calculated using Eq. (1).
e
8 k40 80 12C target 9Be target
nts / 30 60 Jπ Ex SM conf SSM σsp σth σsp σth
u (keV) (mb) (mb) (mb) (mb)
o
C20 40 7/2− 262 [0+⊗1f7/2] 0.425 4.141 1.65 3.905 1.56
10 48Cr 48Cr 20 13//22−− 11770431 [[00++⊗⊗22pp1/2]] 00..234753 00..014104 00..00049 00..003829 00..00039
3/2
0 0 inclusive cross sections: σinc =Σ σj 1.70 1.60
200 600 1000 1400 200 600 1000 1400 th j th
Energy (keV)
reaction model prediction that the 12C-induced pickup
FIG. 2. Doppler-reconstructed γ-ray spectra in coincidence
with 49Mn residues produced in the one-proton pickup reac- proceeds with a slightly higher cross section.
tionsof48Crwith12C(left)and9Be(right)targets. Forboth
targets,theonlyprominenttransitionisthedecayofthefirst
2.0 48Cr+12C 48Cr+9Be
excited 7/2− state to the 5/2− ground state. A peak, stem-
ming from a tail of scattered 48Cr projectiles, is indicated. 7/2- 7/2- 1.5
For the purpose of γ-ray spectroscopy, the software gate was
generous, to include all 49Mn events, and therefore included 1.5
a small amount of 48Cr scattered at large angles.
1.0
1.0
be only weakly populated in the reaction. From the 5/2-
efficiency-corrected peak area relative to the number 5/2- 0.5
of 49Mn produced in the pickup, the partial cross 0.5
section for the population of the 7/2− state could be 1/2- 3/2- 1/2- 3/2-
extracted(σ(7/2−)=1.60(22)mbforthe12Ctargetand
X X X X
σ(7/2−) = 1.43(15) mb for the 9Be target). The partial 0.0 0 261 17031741 0 261 170317410.0
cross section to the 49Mn ground state was derived by
subtraction, i.e. σ(g.s.)=σinc −σ(7/2−). We note that Energy (keV)
exp
the ground-state cross section determined in this way
is an upper limit since some feeding from unobserved FIG. 3. (Color online) Comparison of measured and cal-
culated partial cross sections for proton pickup to 49Mn.
higher-lying proton-unbound states with a γ-ray branch
The DWBA reaction model (see text) and the shell-model
cannot be excluded. We obtain σ(5/2−) ≤ 0.40(25) mb
gs spectroscopic factors from the GXPF1A effective interaction
forthe12C-inducedreactionandσ(5/2−)≤0.20(17)mb
gs are used. The measured partial cross section to the ground
for the 9Be-induced pickup. Due to the significantly staterepresentsanupperlimitobtainedfromthesubtraction
reduced γ-ray detection efficiency at higher energies, σ(g.s)≤σinc −σ(7/2−). The expected higher-lying 2p-shell
exp
we would not have been able to observe γ-ray transi- states are predicted to be populated only very weakly and
tions from the predicted 1/2− and 3/2− states above could not be observed in the present measurement (marked
with x).
1700 keV, the strongest of the two being expected to be
populated at a level of less than 0.04 mb.
Figure3comparesthemeasuredandcalculatedpartial
cross sections for the 12C and 9Be-induced one-proton
pickup to 49Mn. The measured data reproduces the dis- B. Proton pickup to 51Co
tinct population pattern with almost all reactions popu-
latingthefirst7/2−excitedstatein49Mn. Themeasured The most neutron-deficient even-N Co isotope that is
and calculated cross sections, σ(7/2−), agree very well known to be particle bound in its ground state, 51Co,
within the experimental uncertainty for both targets. was first observed in 1987 [31]. The ground state of
The measured inclusive cross section for the 12C tar- this near-dripline nucleus was tentatively assigned to be
get, σinc = 2.00(13) mb, is about 18% higher than the 7/2− [29], with an evaluated proton separation energy
exp
calculated cross section. For the 9Be target, the mea- of only S (51Co) = 90 keV based on systematics [16].
p
sured and calculated inclusive cross sections agree, with This makes 51Co the most weakly-bound nucleus yet
σinc = 1.63(8) mb. The measurement also confirms the studied with a fast one-nucleon pickup reaction. No
exp
7
50Fe+12C 50Fe+9Be
TABLE VI. As Table V but for one-proton pickup to 51Co.
12C target 9Be target
Jπ E SM conf S σ σ σ σ
x SM sp th sp th
0.5
(keV) (mb) (mb) (mb) (mb)
7/2− 0 [0+⊗1f ] 0.246 3.002 0.70 2.858 0.66
7/2
bound or unbound excited states are reported in the lit-
erature for 51Co. Based on the weak binding and the 0.0
non-observation of γ-ray transitions in coincidence with Ground state Ground state
51Co, we assume that, in the experiment, the cross sec-
tion for the population of the (7/2−) ground state ex- FIG. 4. (Color online) Comparison of the measured inclu-
hausts the inclusive cross section. This is unlike the case sive cross section and the calculated partial cross section for
of the one-proton pickup from 22Mg to 23Al [8], where one-proton pickup to the ground state of 51Co. The DWBA
a γ-ray decay of an excited states above the proton sep- reaction model (see text) and the shell-model spectroscopic
aration energy was observed and its contribution to the factor from the GXPF1A effective interaction are used. No
transitions from excited states were observed (S =90 keV).
transfer cross section was included in the calculations. p
The measured inclusive cross sections on the 12C
and 9Be targets are σinc(51Co) = 0.53(13) mb and
exp
σinc(51Co) = 0.57(8) mb, respectively. These are com-
exp
parable in magnitude to the proton pickup cross section of ∆p/p = 1% and (b) the differential momentum loss
to the sd-shell nucleus 23Al, measured on a 9Be target, of the projectile and heavy residue in the thick target.
where σinc = 0.54(5) mb [8]. We note that 23Al is also The latter depends quite sensitively on the interaction
exp
very weakly bound with S (23Al)=142.11(43) keV [32]. pointinthereactiontarget. Thus,deviationsofthemea-
p
Theweakbindingof51Comakesthisnucleustheideal sured reaction residue momentum distributions from the
candidate to study the one-proton pickup into the f momentum profile of the projectile beam having passed
7/2
orbital. As outlined above, we may assume, to a very through the target and folded with the differential mo-
good approximation, that σinc = σ(7/2−). Table VI mentum loss of the mass (Ap+1)-residue – a rectangular
exp
summarizes the shell-model spectroscopic strength for function with a width that takes into account the differ-
the assumed 7/2− configuration and the corresponding enceinmomentumoftheheavyresiduedependingonthe
theoretical cross sections for the population of the 51Co pickupoccurringatthefrontorthebackofthethicktar-
ground state in one-proton pickup from the two targets. get–willindicatenon-two-bodycontributions. Thiswas
In spite of the weak binding and rather small spectro- demonstrated most clearly in Ref. [9], for one-neutron
scopic factor, S =0.246, the cross section is still pre- pickup reactions from a 9Be target, populating excited,
SM
dicted to be of the order of 0.7 mb, which is sizable for unbound 8Be∗ target residues.
the production of such an exotic, weakly-bound nucleus.
Figure 5 shows the measured longitudinal momen-
Figure 4 compares the measured and calculated inclu-
tum distributions of the 49Mn and 51Co pickup reaction
sive cross sections for the (7/2−) ground state of 51Co.
residues produced on the 12C target. Overlayed on the
Measurement and the reaction model predictions agree
figurearealso(i)themomentumprofilesoftheunreacted
within the experimental uncertainty for the 9Be-induced
48Cr and 50Fe projectiles having passed through the tar-
reaction while for the 12C-induced pickup the measure-
get, and (ii) the result after folding these profiles with
ment is about 24% lower than the prediction.
the rectangle function that takes into account the addi-
tionalbroadeningofthedistributionoriginatingfromthe
unknown reaction point in the (thick) reaction target.
C. Momentum distribution diagnostics
As can be seen, after folding the projectile momen-
In earlier work it has been pointed out that the lon- tum profiles with the differential momentum loss expe-
gitudinal momentum distributions of the projectile-like rienced by the residues in the target, the predicted par-
one-nucleon pickup residues can be exploited as an in- allelmomentumdistributionsdescribethemeasureddis-
dicator of contributions to the pickup reaction mecha- tributions very well. Small deviations are visible on the
nism that result in non-two-body final states [9]. This low-momentumsideofthe49Mnmomentumdistribution
diagnostic value arises since, for a strict two-body colli- whereatailstructuredevelops. Thisisinlinewithearlier
sion,thereaction-inducedmomentumdistributionofthe one-proton pickup reaction work on a 9Be target [7] and
residues arising from kinematics and angular deflections one-neutron pickup reaction work on 12C [9], where the
ofthereactionproductsisessentiallyδ-function-likecom- momentum distributions show very little deviation from
paredto(a)themomentumspreadoftheincomingbeam the strict two-body reaction mechanism expectation.
8
pickups from 48Cr to 49Mn and from 50Fe to 51Co were
49Mn 51Co
250 48Cr 50Fe 20 studied, each on both light targets. No bound excited
folded folded final states were observed in 51Co. The measured and
c
V/ 200 C calculated cross sections confirm that the 51Co ground
Me 15ou state is almost certainly a 7/2− state.
n
3 150 ts The measured cross sections were found to agree
31. 10 / 6 well with the two-body reaction model calculations car-
s / 100 2.6 ried out in the distorted waves Born approximation.
unt M Momentum-matching considerations, embedded in the
Co 5 eV reactionmodeldynamics,predictadistinctivepatternof
50 /c finalstatespopulationintheheavyresidues, withatwo-
order of magnitude dominance of pickup into the (cid:96) = 3,
0 0
-400 -200 0 200 400-400 -200 0 200 1f proton orbital compared to pickup into the (cid:96) = 1,
7/2
Δp (MeV/c) 2p orbitals. The49Mnand51Colongitudinalmomentum
|| j
distributions were also used to demonstrate that pickup
FIG. 5. (Color online) Parallel momentum distributions events leading to non-two-body final states could make
(blue symbols) of the 49Mn and 51Co projectile-like residues only very small contributions to the measured reaction
following proton pickup on a 12C target. For comparison, cross sections.
the profiles of the unreacted 48Cr and 50Fe projectiles are The present study complements previous work, on
also shown (red symbols). The red dashed line is a fit to the 9Be-induced one-proton pickup process and the 12C-
these data points. The solid blue line is the result of folding
induced one-neutron pickup reaction, and extends these
the projectile momentum profiles (red dashed lines) with a
studiesintothefp-shell. Theuniqueselectivityofthere-
rectangulardistributionwithawidththatcorrespondstothe
actionmechanismforthepopulationofhigh-(cid:96)overlow-(cid:96)
differentialmomentumlossofthepickupreactionresiduesin
the target, depending on the interaction point. orbitals was clearly shown, reinforcing expectations of
the potential of this reaction as a spectroscopic tool for
the identification of high-(cid:96) intruder states that often in-
dicate the breakdown of shell closures in nuclei far from
stability.
V. SUMMARY AND CONCLUSION
In summary, we have employed intermediate-energy ACKNOWLEDGMENTS
one-proton pickup reactions on 12C and 9Be targets to
study nuclei in the fp-shell. Our experimental approach This work was supported by the National Science
combined thick reaction targets, for luminosity, and γ- Foundation under Grants No. PHY-0606007 and PHY-
ray spectroscopy to tag the final states in the reaction 0758099andbytheUKScienceandTechnologyFacilities
residues. Reactionmodelcalculationsassumingone-step CouncilunderGrantsST/F012012/1andST/J000051/1.
transfersandtwo-bodychannelswereperformed. Proton A.G. is supported by the Alfred P. Sloan Foundation.
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