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Study of the 26Si(p,) 27P Reaction by the Coulomb Dissociation Method Y. Togano

Study of the 26Si(p,) 27P Reaction by the Coulomb Dissociation Method Y. Togano

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550

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



551

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 position-sensitive 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 single-element

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 5-mni-thick AE and 60-nim-thick E plastic scintillators. The momentum vectors of the products were determined by combining

their energies and hit positions on the position-sensitive 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

E-mail: 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 three-body reactions respectively. Their bare

astrophysical S-factors were extracted and from the comparison with the behavior

of the screened direct data, an independent estimate of the screening potential was

obtained.



553



554

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 two-body reaction of interest is carried out from the quasi-free contribution of a suitable three-body

reaction, where the projectileltarget (the so called Trojan Horse nucleus) is

clusterised in terms of the two-body projectile/target and another particle

which plays the role of spectator to the process. In order to overcome the

Coulomb barrier, the three-body 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 two-body reaction

can take place even at very low sub-Coulomb 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 three-body 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 three-body reactions were performed in kinematically complete experiments and the experimental set-ups were optimized in order to cover

the angular regions where the quasi-free process is expected to be favored.

The two-body cross sections were then extracted from the three-body coincidence yields within a spectator momentum window ranging from -30

to t 3 0 MeV/c. Note that the deduced two-body 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 E-100 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/R-matrix 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.



10-2



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+p--t a+a

‘Li+d- a f a

‘Li+p--t ~ 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 2-1 7-1 Fujimi, Chiyoda, Tokyo

102-8160,Japan



HIROYUKI SAGAWA

Center for Mathematical Sciences, the University of A i m Aizu- Wakamatsu,

Fukushima 965-8580, Japan

Neutron skin thickness of stable and unstable nuclei are studied by using Skyrme

Hartree-Fock (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



557



558

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 nucleon-nucleon

potential and a phenomenological three-nucleon interaction, while the long-dashed 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, SIII-IV, 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 nucleon-nucleon potential toIn Figs. l(a)

gether with a phenomenological three nucleon-interaction

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 fm-3. 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 frn-3

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, fi-om 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 neutron-rich nuclei. T h e two nuclei

lo0Sn (filled diamonds) and lS2Pb(open circles) are neutron-deficient. 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 neutron-rich light nuclei while the pressure plays a minor role, although



+



560

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 fm-3

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 mean-field 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



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