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p-TPC: advanced gaseous tracking device

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Figure 2. Obtained 3D proton tracks (closed circles) and their Bragg curves shown in

the cathode=O plane. A typical electron track is also shown by open circles.

3. WIMP-wind detection with p-TPC

Taking into account the tracking capability of the prototype p-TPC and

we calculated the demeasured neutron flux at Kamioka Obser~atory'~,

tection sensitivities of WIMP-wind8. We assume that the track length

and dElcLx threshold of a p T P C as a WIMP-wind detector are 3 inn1 and

10 keV/cm. respectively. F'roni the calculated energy deposition of the F

ion and the scaled track length of the measured va1uel6, we consequently

knew that 25keV F ion has a range of roughly 3mm in 20Torr of CF4.

We also knew that 25 keV Xe ion has a range of roughly 3 mm in 5 Torr of

Xe. The left and right panels of Fig.3 show the SD and SI 3u detection

sensitivities, respectively.

A prototype p-TPC as a WIMP detector with a detection volume

30 x 30 x 30cm3 is now being manufactured. Since the fundamental

manufacturing technology is already established, a large volume detector

( w 1ni3) for the underground measurement will soon be available.

4. Conclusion

We found that p-TPC filled with CF4 gas is a promising device for the

WIMP-wind detection via SD interactions. With even a 0.3 m3. year of

exposure at Kamioka Observatory, it is expected that the best sensitivity

of the current experiments can be achieved. Moreover, it is expected that

the sensitivities of p-TPC as WIMP detector can explore the MSSM region

for SD and SI interactions with a sufficient exposure (- 300ni3 . year).


SD 30 delecllon sensttilies

SI 30 detectionsenstiitles











Figure 3. Estimated SD (left) and SI (right) 30 detection sensitivities at Kamioka

Observatory for three exposures shown by thick solid lines. Limits from the UKDMC

experiment'? are shown by a thin dotted line (left). Limits from other experiment^'^^^^

are shown by thin dotted lines; and DAMA's allowed region2' is shown by a closed

contour (right). Theory regions predicted by minimal supersymmetric extensions of the

) ~ ~also shown in a thin dotted lines (left and right).

standard model ( I v ~ S S Mare


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Centerfor Nuclear Study, Universiw of Tokyo, Hirosawa. Wako. Saitama 351 -0198;



Department ojrlstronomy, University of Tokyo. Hongo, Bunkyo-ku, Tokyo 113-0033

We investigate important reactions and reaction paths in order to reproduce the isotopic

ratios of characteristic elements, C, N, and Si, in presolar Sic grains from novae. We fmd

that the N-isotopic ratio strongly depends on the temperature profile in a nova explosion.

By using this temperature dependence, we obtain a favorable temperature profile during a

nova outburst. Moreover, the calculated 3oSi/28Siratio is high compared with the

observational data of presolar nova grains. We also fmd that this overproduction of 30Si

can be avoided if the reaction rate of '@P(~,y)~'s,which is experimentally still unknown,

could increase by a factor of a few tens around the temperature of -3 X 10* K.



Grains with specific isotopic ratios different from the solar are called 'presolar

grains'. It has been considered that these presolar grains contain a lot of

information about the site of the nucleosynthesis before the formation of the solar

system ','. Understanding the origin of these grains gives us an insight of not only

the synthesized site but also the chemical evolution of the Galaxy '.

The presolar grains are classified into some groups based on their isotopic ratios.

In this investigation, we specifically focus on the so-called 'nova grains', which

were discovered and reported by Arnari et al. '. Although they inferred a

production site as novae from the fact that the isotopic ratios are "C/13C of 4-9,


N/15N of 5-20, high '6Al/'7Al, close-to-solar 29Si/28Si,and a little excess in


Si/"Si, the real origin of nova grains is still questionable. This is because ratios

calculated by hydrodynamical models are largely different from analyzed data,

and the ratios could not be realized by adopting any nova models '. Their results

showed that extra mixing of ejected material with close-to-solar matter is needed

more than 95% after nucleosynthesis ended. However, it is also likely that 'nova

grains' come &om only nova ejecta without such a high mixing rate.

* This work is supported by the fellowship of the Japan Society for Promotion of

Science (JSPS).



Therefore, we re-explore reaction paths during nova nucleosynthesis in detail.

As a result, we find the ideal profile of temperature in order to reproduce the

grain data of 12C/13C,I4N/l5N,and 29Si/28Si.It is also showed that the 3oSi/28Si

ratio can be explained, if the reaction rate of an experimentally unknown reaction,

30P(p,y)3'S,changes by a factor of a few tens. Note that we exclude 26Al/27Alratio

from consideration, since the data of 26A1/27A1

have a large uncertainty '.


Calculations and Parameters for Nova Explosions

We adopt the one-zone model for nova explosions '. When the temperature at the

bottom of the envelope (Tb)is given, the temperature and density structures in the

envelope are determined by a WD mass ( M w ) and an envelope mass (Men,). We

assume an outburst on an ONe white dwarf (WD) because of the overabundance

of 30Si isotope in nova grains. We change the values of M m between 1.15M,

and 1.35 M,, and M,, between 10-j M, and 1O-3.0 M,. These parameter ranges

are necessary to eject the envelope '. We have to mention that this one-zone

model may not be appropriate near the last phase of the nova outburst, since the

envelope is implicitly assumed to be fully convective. Therefore we assume

temperature and density profiles to decay exponentially during the late phase.

It has been generally assumed that the dredged-up matter from the ONe WD is

mixed with the accreted matter from a companion star. The mixing fraction, XwD,

presents the portion of the dredged-up matter in the mixed-matter. A larger value

of XwD means that novae contain a larger amount of heavy elements. We also

treat the mixing fraction as a parameter, whose ranges are between 0.1 and 0.8.



Nucleosynthesis separately occurs in lower and upper regions of the bottle-neck

nuclei with the mass number of A = 19, which have a small proton separation

energy. Each region is related with CNO elements and heavier elements than Ne.

So, we can discuss conditions necessary to reproduce the data of nova grains in

each region, separately. In this paper, we first explain how the temperature profile

is restricted from the temperature dependence of C- and N-isotopic ratios and

secondly we show results from Si-isotopic ratios (for details see Terasawa and

Iwamoto '). We note that these necessary conditions change slightly with values

of XWD,since different values of X ~ mean

D different initial abundances. Here, we

will show an ideal condition in the case of XwD= 0.8.

In nova explosions, Tb becomes high enough to exceed 2 X 10' K, so that HotCNO cycle (HCNO) occurs. In the HCNO cycle, 15N(p,ct)12Cis the key reaction

to determine C and N ratios because of its high reaction rate. The strong

dependence of the reaction rate on the temperature changes rapidly the "N


abundance with temperature. Therefore, "N is transformed to 12C under the

condition with relatively high temperature as soon as 1 5 0 decays into "N.On the

other hand, when the temperature is relatively low, "N remains and thus the


N/"N ratio becomes low. This dependence of the reaction on the temperature

can give a strong constraint on the profile of temperature evolution after "N is

made by the p-decay of "0, that is, at the late phase of explosions. In order to

leave an appropriate amount of "N,it is needed to synthesize "0 abundantly at

the early phase before the p-decay of "0. For this, it is important that the peak

temperature exceeds -2.8 X 10' K. As we described before, since "0 should

decay in the condition with relatively low temperature below -2 X lo8 K, the

decreasing time from the peak to -2 X 10' K is necessary to be about the plifetime of 1 5 0 , 120 sec. Moreover, it is necessary that the temperature is kept in

a range from -2 X 10' K to -10' K in order to preserve the nuclear flow fiom "N

to "C. The duration is favorable to be several thousands of seconds.

As for Si-isotopic ratios, Amari et al. also reported that the 29Si/28Siand

30 . 28 .

Si/ Si ratios are almost the same as the solar. However, both analytical and

hydrodynamical studies 4,' have showed a large enhancement of 30Sirelative to


Si by about a factor of 10. In ONe nova models with high peak temperatures,

the reactions which change the abundances of Si isotopes are known to be the

following eight reactions, 2@Ne(p, y)'lNa, 23Na(p,y)24Mg, 23Mg(p,yy4Al,

28Si(p,Y)'~P, 29Si(p,Y)~OP,29P(p,Y)~OS,30P(p,yY1S, and 31P(p,a)28Si'. Since only

the 3oSi/2*Siratio is large compared with grain data, it is favorable that the 30Si

abundance reduces as the 29Siabundance remains unchanged.

Among above eight reactions, the reaction of 30P(p,y)31Shas large and direct

effects on only 30Si abundance This is because the flow from 28Si to heavier

elements does not go through 29Si, and 30Si are made by P'-decay of 30P at the

late phase. If the reaction rate of 30P(p,y)3'Sbecomes larger by a few tens, the

flow to heavier elements becomes faster. The remaining abundance of 30P

decreases by a few tens. As a result, 30Siabundance reduces and the Si-isotopic

ratios in the nova grains can be reproduced. Moreover, since there has been no

reliable reaction rate for 30P(p,y)31Sdue to the lack of experimental knowledge,

the uncertainty is still a factor of 100 up and down '. Accordingly, it is quite

possible that the reaction rate could be a factor of a few tens higher than the

current rate.

Thus, when its reaction rate becomes higher by a few tens at the temperature

around 3 X 10' K, a good fit is obtained with Si-isotopic ratios measured in nova

grain candidates. For example, we can see a good agreement, 12C/13C= 7.74 and


N/"N = 5.56, in the case of an explosion with MwD= 1.3M,, M,, = 2.5 X

M,, and XwD= 0.8. The reaction rate of 30P(p,y)31Sis multiplied by 20.

At the end, we describe shortly the dependence of temperature profiles on the

value of XwD.We find that it is necessary for the temperature to reach -3.5 X lo8

K in order to make sufficient 29Si in the case of XWD = 0.4. This constraint is

more rigorous than that from the N-isotopic ratio. Thus, synthesis of Si isotopes




imposes a constraint on the peak temperature. When a larger value of XwD is

adopted, the initial abundance of "Si becomes higher. Then, the peak

temperature is allowed to be low. Actually, the peak temperature of 2.8 X 10sK

suffices in the case of X m = 0.8.




We have to mention that the most remarkable difference between

hydrodynamical models and our one-zone models is made at the late phase of

outbursts because of different treatments for convection. However we recognize

that abundances of 12C, "C and ''N strongly depend on the temperature profile at

the late phase. Previous hydrodynamical simulations showed the lower values of

C- and N-isotopic ratios than nova grains '. Based on their results and our results

in which temperature remains relatively high even at the late phase, the inner and

narrow regions in the envelope may be preferable to form the nova grains.

Therefore, nova grains may be seldom found though nova fiequency is relatively

high in our Galaxy (30+ 10 yr-I).


One of the authors (MT) would like to thank Prof. S. Kubono for useful



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Department ofphysics, Universiv of Tokyo, Hongo, Tokyo 113-0033, Japan


The Institute of Physical and Chemical Research (RIKEN), Wako,

Saitama, 351-0198, Japan

The ground state properties of the carbon isotopes are inveshgated usmg the extended

version of the Antisymmetrized Molecular Dynamcs (AMD) Multl Slater Deternunant

method We can reproduce reasonably well many expenmental data for 12C-22CIn this

contribuhon we present a systematic calculation of bmdmg energles, energies of the 2'+

states and B(E2) transition strengths

1. Introduction

The AMD method is very suitable for the description of light systems where

both shell-model and cluster structures can appear because it is free from any

model assumption concerning the wave functions.

The extended version of the AMD method adopted in this work corresponds

to the combination of AMD and the Generator Coordinates Method (GCM)

[l]. The initial GCM basis functions are prepared in such a way that they

correspond to several properly chosen r.m.s. radii constraints, close to the

experimental values.

The mixing amplitudes of these Slater determinants are determined by diagonalization of the Harniltonian matrix. In this way suitable basis for the GCM

calculations can be obtained. The theoretical details of the method are explained

in [2].

2. Results

The Hamiltonian and the effective nucleon-nucleon interaction used is the same

as in [3]. The calculations are performed with 45 and 60 basis functions for


This work is supported by Grant-in Aid for Scientific Research (13740145)

and by The Japanese Society for Promotion of Science under the contract No

On leave of absence from the Nuclear Physics Institute, Czech Academy of

Sciences, Prague-Rez, Czech Republic.



even-even and even-odd isotopes, respectively. The details concerning the basis

hnctions can be found in [2].

The binding energies are presented in Fig. 1. In general, good agreement is

obtained in all the studied region The binding energy of 12C is smaller than the

experimental value. It is partially due to the Majorana parameter M=0.6, fitted

to the binding energy of l 6 0 and known to produce underbinding of I2C. On the

other hand, the spin-orbit term seems to be too strong and thus the 3-alpha

component in the ground state wave function is too small. This is also reflected

in the smaller B(E2) transition strength (see below).

To describe a halo nucleus I5C is a real challenge for the AMD methods.

Here we do not reproduce the ground state spin 1/2+ . This is mainly due to the

simple interaction with no tensor term and strong spin-orbit term. However, in

[2] we have adopted a better description of the s-orbit for the odd neutron and

the excitation energy of the 112' decreased considerabely.

The systematics of the excitation energies of the 2'1 states clearly supports

the idea about N=16 magic number, reflected by large 2fl energy of 22C. The

(dj/2)6subshell closure predicted by our calculation but not seen experimentally

is again due to the stronger spin-orbit term, which pushes the dj/2 orbit down in

energy. A comparison is made with an AMD calculation [4] with weaker spinorbit term and modified Volkov interaction W 1 .

The B(E2 ) transition strengths (Fig.3) are compared with the experimental

data and the shell-model values [5] obtained with effective charges. Smaller

B(E2) value for I2C reflects most probably smaller 3-alpha component in the

ground state wave function due to stronger spin-orbit term. In I6,l8C protons

construct almost closed shell-model configuration so the B(E2) value is very

small. Proton contribution is recovered again in *OC. The very small B(E2) value

for I6C has been measured recently [6] and is successfully reproduced by our


3. Summary

We have performed a systematic AMD+GCM calculation of structure of carbon

isotopes 12C-**C.We can reproduce fairly well a lot of experimental data. Here

we present the systematic calculation of binding energies, 2cI energies and

B(E2) strengths. Even though the effective interaction is simple and there are

indications that the spin-orbit term is too strong it should not change the

qualitative results of this analysis. From the systematics of 2+1 energies a clear

support for the N=16 magic number is given. B(E2) value of 12C is smaller due

to stronger-spin orbit term. Very small B(E2) value for I6C is successhlly

reproduced by our model.

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