Measurements of interaction cross sections for Kr isotopes
26-July-2003
T. Suzuki T. Yamaguchi A. Takisawa 3, L. Chulkov 4, M. Fukuda 5, H. Geissel 2,
M. Golovkov 4, M. Hellström 2, M. Hosoi 1, M. Ivanov 6, R. Janik 6, G. Münzenberg 2,
T. Ohtsubo 2,3, A. Ozawa 7, B. Sitár 6, P. Stremeñ 6, T. Suda 7, K. Sümmerer 2, I. Tanihata 7,
Y. Yamaguchi 3,7
1,
2,
1Saitama
University, Japan
Germany
3Niigata University, Japan
4Kurchatov Inst., Russia
5Osaka University, Japan
6Comenius Univ., Slovak
7RIKEN, Japan
2GSI,
The original proposal of S-250 (Measurements of I of 80,88,96Sr) was approved by 15
shifts at the EA-meeting held at December 2000. However the number of users who may
share the primary beam of 98Mo/124Sn is quite few so far. Thus we would like to replace
the experimental proposal as follows, using 80Kr primary beam.
I. Previous experiments
Measurements of interaction cross-sections (I) at relativistic energies allow us to derive
nuclear matter radii as well as density distributions [1]. Since nuclear matter radii are
directly related to the density distributions, the measurements of I are a good tool to search
for unusual nuclear structures, such as halos and skins. Our group has run three times at the
SIS/FRS facility. Although some part of the data has not been published yet, we have
already presented some references [2-10]. One remarkable finding is the evidence for
proton skins in proton-rich Ar isotopes [10].
One would expect that the proton skin as well as the neutron skin is a quite common phenomenon for nuclei close to the proton or neutron drip line. This expectation agrees with recent predictions obtained by a relativistic mean-field theory [11], a deformed
Hartree-Fock-Bogoliubov model [12] and a spherical Hartree-Fock (SHF) model [13]. In
Fig. 1, R (rp- rn) from Refs. [2,10] are plotted against the difference between the neutron
and proton separation energy (Sp -Sn ) or the Fermi-energy difference (EF). It can be seen
that R has a strong correlation with Sp -Sn. Such a correlation has been predicted by a
relativistic mean-field (RMF) model [1]. However, only proton-rich Ar isotopes and few
other nuclei (20Mg, 17Ne ) are known up to now to have proton-skins [3]. Therefore,
measurements of I for Kr isotopes is expected to provide another example for proton skins.
Fig. 1 Two-dimensional plot of the difference between the proton and neutron separation energies (S p - Sn )
versus the thickness of the nucleon skin R.
Experimental data are from [2] for Na isotopes and [10] for Ar
isotopes, shown by open and closed circles, respectively.
data point.
The corresponding mass number is indicated at each
The shaded area shows the calculated correlation for various isotopes ranging from helium up to
lead [1].
Fig. 2 The difference of rms proton and neutron radii versus the Fermi energy difference (Sp-Sn) for proton rich
Kr isotopes. The prediction of RMF model with NL1 interaction by D. Hirata (private communication).
II.
New proposal
We propose measurements of I for even-mass Kr isotopes, including 72,76,80Kr (Z=36;
N=36, 40,
44), where the charge radii (rc) are available from the isotope-shift
measurements [14]. Moreover, ground state properties such as binding energies and masses,
have been extensively calculated for even-even Kr isotopes in the framework of the
Relativistic Mean-Field Theory [15], by HF+ RPA approach with Skyrme type interactions
[16].
The existence of the neucleon skin in medium mass nuclei implies new collective
isovector modes. In particular, the study of giant resonances (GDR) in exotic nuclei is an
important area of research. GDR strength distributions will be explored nearly to the drip
lines. Recently, a new method for the measurement of the neutron-skin thickness of
unstable nuclei has been suggested by Krasznahorkay et al. [17], using (p, n) reaction in
inverse kinematics. They have demonstrated that there is a predictable correlation between
the isovector spin-dipole resonance (SDR) cross section and the neutron-skin thickness of
nuclei, by measuring the SDR cross sections along the stable Sn isotopic chain. Thus, we can
estimate SDR strength in stead using the eq (3) of Ref. 17, for instance..
The thickness of the proton-skin is expected to be 0.2 fm in 72Kr, as seen in Fig. 2.
Systematic measurements in the same isotopic chain may offer further information for the
creation of proton skins. Since even-even Kr isotopes have excited states with half-lives
shorter than 25 ns (one-fourth of the F1-F2 Time of Flight in the FRS) we may determine I
of the ground state unambiguously. The Kr nuclei are known to be strongly deformed as
shown in Ref. [18]. It was shown earlier by Tanihata et al. that for heavy nuclei rms radii
obtained from I strongly depend on the shape of the density parameterizations. Thus, in
order to derive rms matter radii, we plan to start by using the shape of the charge density
distribution (c(r)) of 88Sr, which is determined from the measurement of 88Sr(e, e) [19].
Another interest in I measurements is to study the nuclear equation of state (EOS) of
asymmetric systems. The number of nucleons (~80) is enough to discuss a collective nature
in nucleus, as discussed in Ref 20, where compressibility and density distributions in ASn
(A=100--160) isotopes are studied. The properties of EOS of symmetric nuclear matter,
such as the saturation density and compressibility, have been studied by a systematic study of
the size, surface diffuseness and binding energy and the giant resonances of nuclei. The
EOS has subsequently been extrapolated to neutron matter for studies of neutron star.
However, no EOS of asymmetric nuclear matter has experimentally been studied so far due
to difficulties of access. Radioactive nuclear beams enable us to study radii of unstable
nuclei over a wide range of relative neutron excess ( = (N - Z )/A ). Together with
isotope-shift measurements, the thickness of neucleon skins can be studied for Kr isotopes in
a wide range of  ( ≤ 0.14). It is pointed out in Ref. [20] that the crucial quantities
determining the neucleon skin are the symmetry energy coefficient (J ) and the neutron skin
stiffness coefficient (Q ). Thus, determination of neucleon-skin thickness as well as of
masses of unstable nuclei would provide a comprehensive data set for these coefficients.
Fig. 3 (Left) Central charge densities against Sp-Sn
(right) for various stable nuclei from 12C to 88Sr . (Right)
Central matter densities for Na isotopes (=20 - 32) [5].
In the left part of fig. 3, central charge densities (co ) for various stable nuclei are plotted
against Sp-Sn , where co determined through the relation of co (r) =  an jo(n r/r*)
using the values of Fourier-Bessel coefficients found in [22]. co does not depend on Sp-Sn
since all the data here are for stable nuclei (i.e.; small Sp-Sn ). However, central matter
densities mo for Na isotopes decrease for larger
|Sp-Sn |> 10 MeV [5]. Although this
tendency is consistent with the decrease in the saturation density for asymmetric nuclear
matter increasing instability [23], the number of nucleons involved is rather small to derive
the central density. Thus, the comparison of the central density (o ) between stable 82Kr
and unstable 72Kr is interesting to see the possible change in the saturation density in
proton-rich nuclear matter. We expect that we may see the effect with an accuracy of
30%. Note that |Sp-Sn | exceeds 10 MeV in 72Kr.
III.
Experimental setup and beam time request
The experimental setup should be identical to our previous experiments [3,6] except for
the TOF start detector at F1 to measure TOF for the section between F1 and F2 in the FRS
(see Fig. 5). We need to identify the mass of incident particle by measuring TOF or . The
required time resolution for the TOF detector should be less than 100 ps. We have already
developed such a TOF detector with a time resolution of 30 ps in FWHM [24]. A clear TOF
separation is expected as shown in fig. 5. The required beam time is summarized in Table-I.
For a proton-rich 72Kr secondary beam, the necessary beam intensity is around 5x108/spill ,
which seems to be possible from the natural abundance of 2.2% for 80Kr, since the achieved
beam intensity and the natural abundance for 86Kr is 4x109 and 17%, respectively.
Be beam production target
Reaction target
F1
F3
F2
F4
ASr
80Kr
TOF1
Plastic Scintillators
TPC
collimators
/spill
IC
MUSIC
Fig. 4 Experimental setup for measuring the interaction cross sections at FRS in GSI [6].
Fig. 5 TOF (for the section F1-F2) separation simulated by MOCADI, where each distribution is convoluted
by the detector resolution of 30ps (FWHM).
Request for beam time (Table I)
Primary beam
80Kr
Fragments
80Kr
itself
Energy
(GeV/u)
Beam time (h)
Total (h)
Empty C target
target
1.05
1
1
2
76Kr
1.05
5
5
10
72Kr
1.05
35
35
70
Setting/
Calibratio
n
2 / 30
Total 120 hours or 15 shifts
References
[1] I. Tanihata et al., Phys. Lett. B 287, 307 (1992).
[2] T. Suzuki et al., Phys. Rev. Lett. 75, 3241 (1995).
[3] L. V. Chulkov et al., Nucl. Phys. A 603, 219 (1996).
[4] O.V. Bochkarev et al., Eur. Phys. J. A 1 15 (1998).
[5] T. Suzuki et al., Nucl. Phys. A 630, 661 (1998).
[6] T. Suzuki et al., Nucl. Phys. A 658, 313 (1999).
[7] A. Ozawa et al., Nucl. Phys. A 673, 411 (2000).
[8] A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000).
[9] L. V. Chulkov et al., Nucl. Phys. A674, 330 (2000).
[10] A. Ozawa et al., Nucl. Phys. A709, 60 (2002).
[11] Z. Ren, Z.Y. Zhu, Y.H.Cai, G. Xu, Phys. Lett. B 380, 241 (1996).
[12] F. Grümmer, B.Q. Chen, Z.Y. Ma, and S.Krewald, Phys. Lett. B 387, 673 (1996).
[13] B.A. Brown and W.A. Richter, Phys. Rev. C 54, 673 (1996).
[14] M. Keim et al., Nucl. Phys. A 586, 219 (1995);
P.Lievens, and the ISOLDE Collaboration Hyperfine Interactions 74, 3 (1992)
[15] G.A. Lalazissis and M.M. Sharma, Nucl. Phys. A 586, 201 (1995)
G.A.Lalazissis, S.Raman, P.Ring, At.Data Nucl.Data Tables 71, 1 (1999).
[16] J.Dobaczewski, W.Nazarewicz, T.R.Werner, Z.Phys. A354, 27 (1996).
P. Sarriguren, E. Moya de Guerra, A. Escuderos, Nucl. Phys. A 658, (1999).
[17] A. Krasznahorkay et al., Phys. Rev. Lett. 82, 3216 (1999).
[18] J.A. Sheikh, J.P. Maharana and Y.K. Gambhir, Phys. Rev. C 48, 192 (1993).
[19] G. Fricke et al, At. Data Nucl. Data Tables 60, 177 (1995).
[20] S.Yoshida, H.Sagawa, N.Takigawa, Phys.Rev. C58, 2796 (1998)
[21] W.D. Myers and W.J. Swiatecki, Phys. Rev. C 57, 3020 (1998).
[22] G. Fricke et al, At. Data Nucl. Data Tables 60, 177 (1995) and
H. De Vries et al., At. Data Nucl. Data Tables 36, 495 (1987)
[23] B. ter Harr and R. Malfliet, Phys. Rev. Lett. 59, 1652 (1987).
[24] M. Chiba et al., RIKEN Accel. Prog. Rep. 36, 71 (2002).