Study of the 26Si(p,) 27P Reaction by the Coulomb Dissociation Method Y. Togano
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24Mg(p,y)25Al(,B+v)25Mg(p,~)z6A1.
This production sequence can be bypassed by 25Al(p,y)26Si(p,y)27P.
It has been suggested that higher temperature novae ( T g FZ 0.4) may be hot enough to establish an equilibrium
between the isomeric state and the ground state of 26A1 Thus, 26Si destruction by proton capture is important to deterniine the amount of' the
gound state of 26A1 produced by the equilibrium, since the isomeric level
of 26AA1would be fed by the 26Si ,B decay. The 27Pproduction in novae
is dominated by resonant capture via the first excited state in 27Pat 1.2
MeV, because the state is close to the Ganiow window. However, there is
no experimental inforniation about the strength of resonant capture in this
reaction. Therefore, we aimed at detrmiining experimentally the ganinm,
decay width of the first excited state in 27P.
'.
Plastic
scintillator
hodoscope
osition sensitive
2.8 m
Figure 1.
Schematic view of the experimental setup.
2. Experimental Setup
The experiment was performed at the RIPS beam line at thc! RIKEN Accelerator Research Facility. A secondary beam of 27Pat 57 MeV/nucleon
was produced by the fragmentation of 115 MeV/nucleoii "Ar beams on a
300 111g/cni2 thick 'Be target. The 27Pbeam bombarded a 125 mg/cni2
thick lead target. A typical intensity and resultant purity were 1.5 kcps
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and 1%,respectively. A schematic view of the setup is shown in Fig. 1.
Products of the breakup reaction, 26Si and proton, were detected in coincidence using a position sensitive silicon telescope and a plastic scintillator
hodoscope. The hit positions of the products and the kinetic energy of 26Si
were measured using the positionsensitive silicon telescope located 50 cm
downstream of the target. The silicon telescope consisted of two layers of
silicon detectors with strips of 5mnl width and two layers of singleelement
silicon detectors. The time of flight of the proton was determined by the
plastic scintillator hodoscope placed 2.8 m dowiistreani of the target. The
hodoscope consisted of 5mnithick AE and 60nimthick E plastic scintillators. The momentum vectors of the products were determined by combining
their energies and hit positions on the positionsensitive silicon telescope.
The relative energy between 26Si and proton was extracted froin the measured momentum vectors of products.
3. Results and Discussions
The relative energy spectrum is shown in Fig. 2. Peaks were observed at
0.34 MeV and 0.8 MeV which correspond respectively to the known first
and the second excited state at 1.2 MeV and 1.6 MeV in 27P‘.
‘OSPb( 27P,p26Si)208Pb
”
0
1
2
3
4
Relative Energy (MeV)
Figure 2. Preliminary relative energy spectrum of the 2G8Pb(”P,p”Si)208Pb reaction.
The peak at 0.34 MeV corresponds to the first excited state in 27Pat 1.2 MeV.
We determined preliminarily the cross section for the first excited state
of 27Pto be 5 nib with a statistical error of about 25%. Supposing the
spin and the parity of the first excited state in 27P is 3/2” from the level
552
schenie of niirror nucleus 27Mg, the transition between the first excited
state and the ground state (1/2+) is by the M1/E2 multipolarities. Since
the E 2 component was strongly enhanced in the Coulomb dissociation 5 , the
experimental cross section is exhausted via the E2 excitation. To extract
the total gamnia decay width, the M1 component was estimated using the
mixing ratio, E2/M1 = 0.043 from the mirror transition in 27Mg '. The
ganinia decay width of the first excited state was determined preliminarily
to be 3.5 f 0.6 nieV. This result is consistent with the vdue estimated on
the basis of a shell model calculation '. It indicates that the 26Si(p,y)27P
reaction does not contribute significantly to the amount of the ground state
of 26A1in novae.
4. Summary
We determined experimentally the garnnia decay width of the first excited
state in 27P.The obtained width is 3.5 f 0.6 meV, showing consistency
with t,he shell niodel calculation. This value indicates that this reaction
does not play an important role t o control the amount of 26A1in novae.
References
N. Prantzos and R. Diehi, Phys. Rep. 267, 1 (1995).
A. COC,M.G. Poryuet, and F. Nowacki, Phys. Reu. C 61, 015801 (1999).
T. Kubo et al., Nucl. Instr. Meth. B70, 309 (1992).
J. A. Caggiano et al., Phys. Reo. C 64, 025802 (2001).
5. T. Motobayashi et al., Phys. Rev. Lett. 73 2680 (1994).
6. M. J. A. de Voigt et al., Nucl. Phys. A186, 365 (1972).
1.
2.
3.
4.
THE TROJAN HORSE METHOD APPLIED TO THE
ASTROPHYSICALLY RELEVANT PROTON CAPTURE
REACTIONS ON Li ISOTOPES
A. TUMINO, C. SPITALERI, A. MUSUMARRA, M. G. PELLEGRITI, R. G.
PIZZONE, A. RINOLLO AND S. ROMANO
Dipartimento d i Metodologie Chimiche e Fisiche per l’tngegneria, Uniuersitd d i
Catania and Laboratori Nazionali del Sud  INFN
Via S. Sofia, 44
95123 Catania, I T A L Y
Email: tumino @lns.infn.it
L. PAPPALARDO
Texas A M University,
College Station, T E X A S  USA
C. BONOMO, A. DEL ZOPPO, A. DI PIETRO, P. FIGUERA
Laboratori Nazionali del Sud  INFN, Catania, I T A L Y
M. LA COGNATA, L. LAMIA
Centro Siciliano di Fisica Nucleare e Struttura della Materia, Catania and
Laboratori Nazionali del Sud  INFN, Catania, I T A L Y
S. CHERUBINI AND C. ROLFS
Ruhr Universitaet,
Bochum, G E R M A N Y
S. T Y P E L
GSI mbH,
Darmstadt. G E R M A N Y
T h e 7Li(p,a)4He ‘Li(d,a)4He and ‘ L i ( ~ , a ) ~ Hreactions
e
was performed and studied in the framework of the Trojan Horse Method applied t o the d(7Li,aor)n,
‘Li(‘Li,a~x)~Heand d(‘Li,a3He)n threebody reactions respectively. Their bare
astrophysical Sfactors were extracted and from the comparison with the behavior
of the screened direct data, an independent estimate of the screening potential was
obtained.
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1. General I n t r o d u c t i o n
Measurements of Li abundances contribute to the study of different fields as
Big Bang nucleosynthesis, cosmic ray physics and stellar structure. Within
these fields the knowledge of thermonuclear reaction rates for reactions producing or destroying Li isotopes turns out to be very important. However,
due to the Coulomb barrier suppression in the entrance channel and to the
electron screening at very low energy, the determination of the relevant astrophysical bare nucleus S(E) factor can be carried out only through the
extrapolation from the higher energies
A complementary way to get
the bare nucleus Sb(E) factor is given by the Trojan Horse Method (THM),
which allows to measure the energy dependence of Sb(E) down to the astrophysical energies free of Coulomb suppression and electron screening
effects
The Sb(E) information for the twobody reaction of interest is carried out from the quasifree contribution of a suitable threebody
reaction, where the projectileltarget (the so called Trojan Horse nucleus) is
clusterised in terms of the twobody projectile/target and another particle
which plays the role of spectator to the process. In order to overcome the
Coulomb barrier, the threebody reaction takes place at high energy. Then
this energy is compensated for by the binding energy of the two clusters
inside the Trojan Horse nucleus, in such a way that the twobody reaction
can take place even at very low subCoulomb energies 7.
'i2.
37475967778.
2. Experimental details and r e s u l t s
The THM was applied to the d(7Li,a a ) n , 'Li('Li,a ~ x ) ~ H
and
e d('L1,a
3He)n threebody reactions in order to study the astrophysically relevant
7Li(p ,a)4
He 6Li(d,a)4He and 6Li(~ , a ) ~ H
twoe body reactions
The threebody reactions were performed in kinematically complete experiments and the experimental setups were optimized in order to cover
the angular regions where the quasifree process is expected to be favored.
The twobody cross sections were then extracted from the threebody coincidence yields within a spectator momentum window ranging from 30
to t 3 0 MeV/c. Note that the deduced twobody cross sections are the
nuclear part alone, this being the main feature of the THM. In order to
deduce the experimental S(E) factors from the standard definition, the nuclear cross sections were multiplied by the proper transmission coefficient
Tl(E). The extracted S(E) factors for the three reactions are shown in figs. 1
(7Li(p,o)4He),2(6Li(d,a)4He),3 ( ' L i ( ~ , a ) ~ H e(full
) dots) superimposed to
direct data from ref.
(open symbols). The normalization to the direct
314,5967778.
','
555
data was performed in an energy region were screening effects on the direct
measurements are negligible. At energy above E100 keV the agreement
between the two sets of data is quite good, while they disagree at lower
energies as expected, thus fully supporting the validity of the THM. Once
parameterized the two behaviors, it was possible to get also independent estimates of the screening potential for the Li+H isotopic pair. The resulting
values for the three reactions, together with the S(0) parameters extracted
from second order polynomial fits/Rmatrix calculations on the data are
reported in Table 1. Values from direct experiments are also quoted. Our
results affected by smaller uncertainties than direct data agree with both
the extrapolated S(0) and U, direct estimates. Moreover our U, estimates
confirm within the experimental errors the isotopical independence of the
screening potential. The large discrepancy (about a factor 2) with the
adiabatic limit (186 eV) is still present.
102
lo’
L.(MeV)
Figure 1. S(E) factor for the 7Li(p,a)4He reaction. Full dots represent THM data,
open symbols refer t o direct d a t a of ref.’. The solid line is the result of a second order
polynomial expansion which gives the S(0) value reported in Table 1.
Table 1. S(0) and U, values from THM and direct experiments for 7Li(p,a)4He 6Li(d,a)4He
and ‘ L i ( ~ , a ) ~ Hreactions.
e
7Li+pt a+a
‘Li+d a f a
‘Li+pt ~ x + ~ H e
S(0) THM [MeV b]
0.055f0.003
16.9f0.5
3.00f0.19
S(0) Dir. [MeV b]
0.058
17.4
2.97
U, THM [eV]
3301k40
340f50
450f100
U, Dir. [eV]
300f160
330f120
440f160
556
L m .
Figure 2.
( Mev>
S(E) factor for the 6Li(d,cu)4Hereaction. Same description as fig.1.
A?
n
‘Li( p, ~ x ) ~ H e
Figure 3.
S(E) factor for the ‘ L i ( ~ , a ) ~ Hreaction.
e
Same description a s fig.1
References
1.
2.
3.
4.
5.
6.
7.
8.
S. Enstler et al., 2.Phys. A342, 471 (1992).
C. Angulo et al., Nucl. Phys. A656, 3 (1999).
C. Spitaleri et al., Phys. Rev. C60, 55802 (1999).
C. Spitaleri et al., EUT. Phys. J o u m . A7 181 (2000).
C. Spitaleri et al., Phys. Rev. C63 055801 (2001).
M. Lattuada et al., A p J 562 1076 (2001).
A. Tumino et al., Phys. Rev. C67 (2003).
A. Tumino et al., Nucl: Phys. A718, 499 (2003).
NEUTRON SKIN A N D EQUATION OF STATE IN
ASYMMETRIC NUCLEAR MATTER
SATOSHI YOSHIDA
Science Research Center, Hosei University 21 71 Fujimi, Chiyoda, Tokyo
1028160,Japan
HIROYUKI SAGAWA
Center for Mathematical Sciences, the University of A i m Aizu Wakamatsu,
Fukushima 9658580, Japan
Neutron skin thickness of stable and unstable nuclei are studied by using Skyrme
HartreeFock (SHF) models and relativistic mean field (RMF) models in relation
with the pressure of EOS in neutron matter. We found a clear linear correlation
between the neutron skin sizes in heavy nuclei, "*Sn and "'Pb and the pressure
of neutron matter in both SHF and RMF, while the correlation is weak in unstable
nuclei 32Mgand "Ar.
1. Equation of state and pressure for neutron matter
The size of the neutron skin thickness will give an important constraint on
the pressure of the equation of state (EOS), which is an essential ingredient
for the calculation of the properties of neutron stars
T h e pressure P of
neutron matter is defined as the first derivative of Hamiltonian density by
the neutron density,
where H is the Hamiltonian density of neutron matter H ( p n , p p = 0). In
this Hamiltonian density for infinite nuclear matter, the derivative terms
and Coulomb term are neglected. Whereas the spherical symmetry is assumed in finite nuclei. The neutron skin is defined by the difference between
the root mean square neutron and proton radii,
Fig. l(a) shows the neutron equations of state for our different parameter sets, while the pressure of neutron matter is plotted as a function of
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13 14
SO
IS i n
s
3
13 14
50
7
40
40
I1

8
'
5 30
h
E:
211


30
9
.2s
20
E
_620
u
w
2
e
10
I
10
0
4
0
0.00
0.10
0.20
030
10
0.00
0.20
0.10
030
pn ( f m J )
Figure 1. (a) The neutron equations of state are shown for the 1 2 parameter sets of
the SHF model (solid lines) a n d 3 parameter sets of the R M F model (dashed lines).
Filled circles correspond t o the variational calculations using the V 1 4 nucleonnucleon
potential and a phenomenological threenucleon interaction, while the longdashed curve
corresponds t o the SGII interaction. (b) T h e pressure of neutron matter as a function of
neutron densities. T h e numbers are a shorthand notation for the different interactions:
1 for SI, 2 for SIII,3 for SIV, 4 for SVI, 5 for Skya, 6 for SkM, 7 for SkM', 8 for SLy4, 9
for MSkA, 10 for SkI3, 11 for SkT4, 12 for SkX, 13 for NLSH, 14 for NL3, 15 for NLC,
20 for SGII.
neutron density in Fig. l(b). In Figs. l(a) and l ( b ) the solid and dotted
lines show the results with SHF and RMF models, respectively. We present
results obtained with 13 SHF parameter sets ( SI, SIIIIV, SVI, Skya, SkM,
SkM*,SkI3, SkI4, MSkA, SLy4, SkX, SGII ) and 3 RMF parameter sets (
NL3, NLSH, NLC ). We plot the results obtained with SGII in Figs. l ( a )
and l ( b ) , since the SGII interaction gives almost equivalent results to those
of the variational calculations using the 2'14 nucleonnucleon potential toIn Figs. l(a)
gether with a phenomenological three nucleoninteraction
and l ( b ) one can see large variations among different parameter sets. A
general feature is t h a t the RMF curves exhibit a much larger curvature
than do the SHF curves, some of which even have negative curvature. Figs.
l(a) and l ( b ) show that results obtained with the SGII and SkX parameter
sets are almost equivalent to the results of the variational calculations.
Next, we study the relation between the neutron skin thickness of finite
nuclei and the pressures of neutron matter at pn = 0.1 fm3. Results for
the pressures a t pn = 0.1 fmW3and are given in Figs. 2(a) and 2(b), respectively. The properties of nuclear matter a t high densities are important
'.
559
030
14
0
3*
0.25
l5
10
0
1

%E030
10
0
n
CL
x
0.15

v
Loc
0.10
4
2
0
0
0
20
Lo
0 1
0.15
(4
0.05
(
0.5
I .O
0.10
0.0
1.5
P ( pn=O.l frn.' ) ( MeV frn" )
Figure 2. The correlations between the pressures of neutron matter at h = 0.1 frn3
and the neutron skin thickness obtained with the SHF (open circles) and R M F (filled
circles) parameter sets. (a) the result for "'Pb.
(b) the result for lJ2Sn. See the caption
to Fig. 1 for details.
for a unified description of neutron stars, fiom the outer crust down to the
dense core '. Clear linear correlations are found between the neutron skin
thickness S
, and the pressure P of 208Pb and 132Snin Figs. 2(a) and 2(b),
respectively, with the parameter sets of the SHF and RMF models used in
Figs. l(a) and l ( b ) . We checked that there are same linear correlations a t
In general, the RMF presnot only pn = 0.1 fm' but also pn = 0.2 frn'.
sures are larger than those of SHF models, and the RMF models give the
larger neutron skin thickness. Thus, experimental 6,, values would provide
important constraints on the parameters used in SHF a n d RMF models.
We also study the relation between the pressure and the neutron skin
thickness of several other nuclei, namely "Mg, 38Ar, 44ArI lo0Sn, 138Ba,
'"Pb and '14Pb obtained in SHF
BCS calculations. In Fig. 3, 38Ar
(filled triangles), '"Ba (crosses) and "'Pb (filled circles) are stable nuclei,
whereas 32Mg (reversed open triangles), 44Ar (open triangles), '32Sn (open
diamonds) and '14Pb (open squares) are neutronrich nuclei. T h e two nuclei
lo0Sn (filled diamonds) and lS2Pb(open circles) are neutrondeficient. This
figure shows, in general, that the higher the 3rd component of the nuclear
isospin T, = ( N  2 ) / 2 is, the steeper the slope of the line is. This isospin
rule does not hold in 32Mg. This is because the effect of the neutronproton Fermi energy disparity dominates the increase in the neutron radii
of neutronrich light nuclei while the pressure plays a minor role, although
+
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the absolute magnitude of S
, is the largest in Fig. 3. The configuration
mixing might play a n important role in determining the neutron and proton
radii in 32Mg. However,the correlation between the neutron skin thickness
and the pressure might not be changed by configuration mixing.
Figure 3. The correlations between the
pressures of neutron matter and the neutron skin thickness of 3ZMg(reversedopen
triangles) Ar( filled triangles) ," Ar( open
triangles),lOOSn(filleddiamonds), 13'Sn
(open diamonds),138Ba(crosses),182Pb(open
circles), 208Pb(fillcd circles) ?''Pb( open
squares) for the pressure at pn = 0.1 fm3
obtained by SHF parameter sets. See the
caption t o Fig. 1 for details.
I
t
U.1l
115
0.5
1.0
I .5
P ( pn=O.I fm" ) ( hleV fmJ )
2. Summary
We studied relations between the neutron skin thickness and the pressure
of the EOS in neutron matter obtained in SHF and RMF models. A strong
linear correlation between the neutron skin thickness and the pressure of
neutron matter as given by the EOS is obtained for stable nuclei such
as 132Sn and '08Pb. On the other hand, the correlations between the two
quantities in unstable nuclei such as "Mg and 44Ar are found to be weaker.
We pointed out that i n general the pressure derived from the R M F model
is much higher than that obtained from the SHF model. Also the neutron
skin thickness of both stable and unstable nuclei is much larger in the
RMF models than in the SHF models for stable nuclei. Thus, experimental
d a t a on the neutron skin thickness gives critical information both on the
EOS pressure in neutron matter and on the relative merits of the various
parameter sets used in meanfield models '.
References
1. C.J. Horowitz and J . Piekarewicz, Phys. Rev. Lett. 86, 5647 (2001).
2. B. Friedman, and V.R. Pandharipande, Nucl. Phys. A361, 502 (1981).
3. G. Baym, H.A. Bethe and C.J. Pethick, Nucl. Phys. A175,225 (1971).
4. S. Yoshida and H. Sagawa, Phys. Rev. C 6 9 , (2004) to be published