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N 238U + natU heavy ion reaction using muscovite mica track detector
Nucl
Pergamon
Trat~ P,,d;,- Meas, Vol.22, Nm i-4, pp. 633--636, 1993 inserter ScieaeeLtd Prm~ in Omstarimm. 0969-SOTS/~$6.00+.00
STUDY OF 14.2 MeV/N 23sU + *JU HEAVY ION REACTION USING MUSCOVITE MICA TRACK DETECTOR ZHOUPEI-DE.* GUOSm-Lvs,* R. B~a~Drt and P. VAT, S *China Instituteof AtormcEnergy,Beqmg 102413, China; tKemehermeFB14, Umver~ttyMarburg, D-3550 Marburg. Germany
ABSTRACT The heavy ion reaction of 14.2 M c v / N m U + " t i t has been studied using muscovite mica track detector and 2=---geometry detection technique. The reaction cross section and the partial cross sections of 3, 4 and $ massive fragments (each not less than 30u) exit channels have been obtained. The masses and energies of the fragments have been celculatud -___oo3rdingto the spherical coordinates of the tracks formed by the multifragments using the quantitative analysing methodology developed by P.A.Gottsehalk et al. and the standard velocity--range data. Then the kinematical analysis on each selected event has been performed and it shows that the main reaction channel of 14.2 Mev / N U+U is the sequential fission of projectile--like or / and target-like nuclei resulting from inelastic or deep inelastic collision. Some features of the sequential fission have been drawn. KEYWORDS m U with ~ U reaction; mica track detector; multipron8 event; massive fragment; sequential fission. INTRODUCTION This work is one of the series of study in which reactions of heavy projectiles with heavy targets are studied with solid state nuclear track detectors0-6). With the advent of heavy ion accelerator like UNILAC in GSI, Darmstadt, Germany, a strong interest emerged to study the interactions of heavy proiectiles with bevy targets. Such experiments provide unique opportunity to study the transfer of large amount of energy, mass and angular momentum in deep elastic collisions, the subsequent relaxation phenomena, such as sequential fiuion and the structure of nuclei at high excitation energy(4). EXPERIMENTAL METHODS Mice track detector in 2x-geometry °3 was used in this study, The target material utU, in the form of UF4, was vacuum deposited on the surfa~ of muscovite mice. The t a r p t thickness is 1.14mg / cm a, which was determined by weighing the mica before and after the deposition. The tarlet area is 12.9 cm~(about 4cm in diameter). Samples so prepared are then irradiated with 14.2 Mcv / N ~ heavy ions from the accelerator UNILAC. The direction of heavy ion beam was perpendicular to the surface of mica detector. The fluence of heavy ions irradiated on the target is (2.00± 0.08) x 106cm-a, which was determined by the •real density of tracks of projectiles on the surface of the mica detector. After irradiation, The target material was dissolved away with HNO 3 and the mica detector was etched with 48"/, HI= at room temperature for 13 minutes. After etching, the tracks of projectiles and reaction products can be seen clearly with optical microscope. The former arc round black dots, the latter •re 2-, 3-, 4 - and S-prong events. An optical microscope was used to count the projectile tracks and to measure the length and angle of each track in • multiprons event.
~.am n ,-+--w
633
634
ZHOU PEI-DE eta/. RESULTS OF CROSS SECTIONS
The following formular was used to calculate the cross section ~l: ¢~= N ~ / ( 0 • A • S)
(I)
where N I is the number of events having i-prong tracks, @ is the projectile fluence measured from the areal density o f the round black dots, A is the number of target nuclei in unit area o f the target and S is the targrt area. The results of cross section are listed in Table 1. Table 1. Measured cross sections of multiprong events E n e r g y ( M e V / N)
14.2
¢~ Co)
04CO)
O"5 Co)
0"3+4+5('0)
2.90+0.37
1.86±0.26
0.09±0.04
4.85±0.57
T H E O R E T I C A L CALCULATIONS OF CROSS SECTIONS Thu data of elastic two prong events arc used to calibrate the parameters of tracks and to calculate the reaction c r o u section based on quarter point angle 01/4. The e l / 4 in this r u c t i o n is 34" ± 4 " , that is the angle at which the expm~nental elastic scattering cross section is one fourth of the a v e r a F M O T T Icattexing ~oss section. According to Blairs quarter point recipe, the reaction cross ruction can be predicted using the following expefisons.
L,, - ,tcot(l 0,)¢~-~(1
l.,.
=+1) a
(2) (3)
where q is the Sommcrfeld parameter and ~ is the asymptotic wavelength of relative motion. The reaction cross section can be prcdicted by sharp cut-ofT model ~n also. Table 2 provides the comparison o f model calculation ¢ z j to experimental reaction cross section c z ~ e and era.n/4. Table 2. Comparison of model calculation cross section(¢r~) to experlmcntal rcsults(ur.3+a+s, ur.s/4)
4.852 ::1:0.567
4.378 ± 0.832
4.889
Since the experimental reaction cross section determined with two different and independent methods are in aFcmncnt to each other and to th© model calculation, it can bc concluded that the emissions of 3, 4 and 5 fragments in exit channel exhaust the reaction c~oss m~tion. Above aBn~ment ensures that almost all the events o f various multiplicities have been detected and observed. Hence the partial reaction cross section ¢3, ¢4 and cs co~fld be experimentally determined. ANALYSIS OF MULTI'FRAGMENT EVENTS With the help of the measured track lenf~.hs and angles of each multiprong event, the kinematic process o f nuclear interactions can bc reconstructed using the computer program P R O N G Y (@. The mmntial inlpredents of this program arc a veiocity-ranlps relationship and the coupled equations for momentum conm'vation, i.e. |
4
v(m,O- z z o m $ wmO
C re'i"
(4)
635
STUDY OF 14.2 MeV/N 23SU + ~ U
~m,,(~. J).- e..
O3
J
Y.ml-m
+m ~
(if
I >
(63
2)
I
where m,v,l are mass, velocity and track length o f the fragment, mp and m t are projectile and t a r F t mass, respectively. P~. is incident momentum. The coefficients C~, are determined by a calibration procedure which has been discussed in detail in referencesO'4}. We used the parameters of about 400 elastic two prongs events to calibrate the coefl'udents of C~. The values of C.v calibrated by this method are listed in Table 3. Table 3. Coefficients of C,, from elastic two prongs events Cur
v=0
v=l
v=2
v=3
v=4
u =, 0
1.134E-1
1.379E-2
2.848E-3
-2.124E-4
4.042E-6
u- 1
-1.380E-3
3.252E--4
-3.028E-5
1.082E-6
-1.411E-8
u=2
4.006E-6
-1.199E-6
1.049E-7
-3~221E-9
2.978E-11
This set of coefficients C,, were used to analyse the multifragment events. Table 4 lists the numbers of events which we measured. Table 4. Numbers of events treated in this work 3-prongs events
4-prongS events
5-prongs events
direct
107
50
4
indirect
57
55
1
total
164
105
5
measured(I)
98
38
--
analysed(2)
83
2.5
--
selected(3)
73
21
--
In our study we found that only a part of direct multiprongs events could be measured for obtaining their complete track lengths. Only about 1 / 3 of total events could be analysed by using the coefficients Cur and only a part of the analysed events could fit into the framework 1.9 ~ V , , ~ 3 . 1 cm / nsec, which is the characteristic velocity between two fragments in nuclear fission. The final fragment mass distribution of selected 3-prongs events are Gauss/an shape, integsrated over all enersies and angsles. Two fission fragments with m , = 9 5 + 33u and mr= 153 + 30u and one surv/ring fragment ink= 210 ± 40U are observed. Here one of the uranium nuclei, after experiencings a nuclear collision and handing over a net amount of mass to the other, survives fission. The compl~nentary particle fissions in the second step of the reaction and yields two typical f'm/on fraj. ments. The sum o f the correlated fission fragment masses (m i and mj)have an averafp; value o f 252± 32u, representing the mass of one intermediate nuclei which would undergo fission sequentially. The T K E L can be deduced, event by event, from the expression TKEL - E~
-- ( ~ E I - E t)
(7)
636
ZHOU PEI-DE
et aL
m,mlV ~ E r " 2(m, + m l )
(n
-
3)
(S)
(n > 3)
(9)
or
E-
F2 t I q.
m m
mtmiF'~
r 2(m, + ml7 + 2(m, + m,)
E, is the kinetic energy assoeiated to each track. The kinetic energy available above the entrance coulomb barrier (P..,,,,) is 955Mev in the present reaction. Some events which T K E L is hurj~ than have been observed experimentally. It shows that the effects ofdetormation and mass or charlie transfer of the intermediate fragments formed in the first reaction step must be taken into account for tome events. In order to study the sequential fission process further, for example, reamnable explanation concerning the relative high amount of three prong events in the reaction channel and higher energy damping, it is on the right way to examine the mass transfer in detail. According to the mass transfer distributions of selected 3-prong events in the three T K E L intervals, (a)-l$0 ~300Mev, (b)300,- 600Mev, (c)600-- 900Mev, we known that the mean mass tranffer in case of the deep inelastic collision is larger as compared to that in less damped reactions. The largest mass transfer with a mean value of 38± 18u has been observed for three prong events in the highest T K E L re,. gion.
If mass transfer is larger, one oftbe intermed/ate nuclei is too light or its intrinsic excitation energy is too low such that the probability to undergu rission is small and there/ore this intermed/ate mass survives, and this process yields three final masses. CONCLUSION The reaction cross sections determined with theoretical and experimental methods arc in good NFeement. We could say that the main react/on channel of the reaction in the incident energy studied is multifragment emission after collisions of the projectiles and target nuclei. According to quantitative analyses, most of the multifragment events are resulted form sequential fission after inelastic collision of" the projectiles and target nuclei. After inelastic collision, one or two uranium undergo fission to appear as 3-, 4 - or 5-prong events, respectively. The er3/ ~4 value and the higher mass transfer at h/ghest TKEL region shows a tend that when fully damp reaction occurred it is most probable to yieid 3 fmal masses and in high projectile energy the cross sect/on of fully damp reaction is qunt/tetively larger. It is my pleasure to thank Prof. Gun Shi-Lun for his guidance and Prof. Dr. R.Brandt and Dr. P.Vater, Marburg University for their kind cooperation. I am indebted to Dr. l.B.Qureshi for guilding the use of the program PRONOY and Dr. F.Hubert for providing the projram calaulating the stopping power and range. REFERENCES
1. Durrani, S.A. and Bull, R.K. (1957). Solid State Nuclear Track Detsction --Principics, Methods and Applicatons, England. 2. Khan, E.U~(1989). Ph.D. Thesis, Study of the heavy ion reaction =e13+~WUat the beam eaer~km of 9.0 and 16.7 Mev / N using mica as solid state nuclear track detector. 3. Khan, H.A. (1964-1989). Selected Research , .Publ/cat/onsofDrJ-I.A.Khan. 4. Gottschalk, P.A. and Grawer~ G. (1983). Physics Review, C27. 5. Vater, P. ~ al. (1977). Nuclear .Instrum.ent and Methods, 147. 6. Brandt, R. et al. (1980). Nuclear TnsU'llJm(~trand M(~,, o~., ~.73. 7. Bast, R. (1980). Nuclear Reaction s With fleavy Ions, Berlin. 8. Hubert, F. etal. (1990). R a n p and Stopping-Power Tables for 2 . 5 - $ 0 0 M e v / N Heavy Ions in Solids, Atomic Data and Nuclear Data Tabics, Vol.~_., N0.1.
Pergamon
Trat~ P,,d;,- Meas, Vol.22, Nm i-4, pp. 633--636, 1993 inserter ScieaeeLtd Prm~ in Omstarimm. 0969-SOTS/~$6.00+.00
STUDY OF 14.2 MeV/N 23sU + *JU HEAVY ION REACTION USING MUSCOVITE MICA TRACK DETECTOR ZHOUPEI-DE.* GUOSm-Lvs,* R. B~a~Drt and P. VAT, S *China Instituteof AtormcEnergy,Beqmg 102413, China; tKemehermeFB14, Umver~ttyMarburg, D-3550 Marburg. Germany
ABSTRACT The heavy ion reaction of 14.2 M c v / N m U + " t i t has been studied using muscovite mica track detector and 2=---geometry detection technique. The reaction cross section and the partial cross sections of 3, 4 and $ massive fragments (each not less than 30u) exit channels have been obtained. The masses and energies of the fragments have been celculatud -___oo3rdingto the spherical coordinates of the tracks formed by the multifragments using the quantitative analysing methodology developed by P.A.Gottsehalk et al. and the standard velocity--range data. Then the kinematical analysis on each selected event has been performed and it shows that the main reaction channel of 14.2 Mev / N U+U is the sequential fission of projectile--like or / and target-like nuclei resulting from inelastic or deep inelastic collision. Some features of the sequential fission have been drawn. KEYWORDS m U with ~ U reaction; mica track detector; multipron8 event; massive fragment; sequential fission. INTRODUCTION This work is one of the series of study in which reactions of heavy projectiles with heavy targets are studied with solid state nuclear track detectors0-6). With the advent of heavy ion accelerator like UNILAC in GSI, Darmstadt, Germany, a strong interest emerged to study the interactions of heavy proiectiles with bevy targets. Such experiments provide unique opportunity to study the transfer of large amount of energy, mass and angular momentum in deep elastic collisions, the subsequent relaxation phenomena, such as sequential fiuion and the structure of nuclei at high excitation energy(4). EXPERIMENTAL METHODS Mice track detector in 2x-geometry °3 was used in this study, The target material utU, in the form of UF4, was vacuum deposited on the surfa~ of muscovite mice. The t a r p t thickness is 1.14mg / cm a, which was determined by weighing the mica before and after the deposition. The tarlet area is 12.9 cm~(about 4cm in diameter). Samples so prepared are then irradiated with 14.2 Mcv / N ~ heavy ions from the accelerator UNILAC. The direction of heavy ion beam was perpendicular to the surface of mica detector. The fluence of heavy ions irradiated on the target is (2.00± 0.08) x 106cm-a, which was determined by the •real density of tracks of projectiles on the surface of the mica detector. After irradiation, The target material was dissolved away with HNO 3 and the mica detector was etched with 48"/, HI= at room temperature for 13 minutes. After etching, the tracks of projectiles and reaction products can be seen clearly with optical microscope. The former arc round black dots, the latter •re 2-, 3-, 4 - and S-prong events. An optical microscope was used to count the projectile tracks and to measure the length and angle of each track in • multiprons event.
~.am n ,-+--w
633
634
ZHOU PEI-DE eta/. RESULTS OF CROSS SECTIONS
The following formular was used to calculate the cross section ~l: ¢~= N ~ / ( 0 • A • S)
(I)
where N I is the number of events having i-prong tracks, @ is the projectile fluence measured from the areal density o f the round black dots, A is the number of target nuclei in unit area o f the target and S is the targrt area. The results of cross section are listed in Table 1. Table 1. Measured cross sections of multiprong events E n e r g y ( M e V / N)
14.2
¢~ Co)
04CO)
O"5 Co)
0"3+4+5('0)
2.90+0.37
1.86±0.26
0.09±0.04
4.85±0.57
T H E O R E T I C A L CALCULATIONS OF CROSS SECTIONS Thu data of elastic two prong events arc used to calibrate the parameters of tracks and to calculate the reaction c r o u section based on quarter point angle 01/4. The e l / 4 in this r u c t i o n is 34" ± 4 " , that is the angle at which the expm~nental elastic scattering cross section is one fourth of the a v e r a F M O T T Icattexing ~oss section. According to Blairs quarter point recipe, the reaction cross ruction can be predicted using the following expefisons.
L,, - ,tcot(l 0,)¢~-~(1
l.,.
=+1) a
(2) (3)
where q is the Sommcrfeld parameter and ~ is the asymptotic wavelength of relative motion. The reaction cross section can be prcdicted by sharp cut-ofT model ~n also. Table 2 provides the comparison o f model calculation ¢ z j to experimental reaction cross section c z ~ e and era.n/4. Table 2. Comparison of model calculation cross section(¢r~) to experlmcntal rcsults(ur.3+a+s, ur.s/4)
4.852 ::1:0.567
4.378 ± 0.832
4.889
Since the experimental reaction cross section determined with two different and independent methods are in aFcmncnt to each other and to th© model calculation, it can bc concluded that the emissions of 3, 4 and 5 fragments in exit channel exhaust the reaction c~oss m~tion. Above aBn~ment ensures that almost all the events o f various multiplicities have been detected and observed. Hence the partial reaction cross section ¢3, ¢4 and cs co~fld be experimentally determined. ANALYSIS OF MULTI'FRAGMENT EVENTS With the help of the measured track lenf~.hs and angles of each multiprong event, the kinematic process o f nuclear interactions can bc reconstructed using the computer program P R O N G Y (@. The mmntial inlpredents of this program arc a veiocity-ranlps relationship and the coupled equations for momentum conm'vation, i.e. |
4
v(m,O- z z o m $ wmO
C re'i"
(4)
635
STUDY OF 14.2 MeV/N 23SU + ~ U
~m,,(~. J).- e..
O3
J
Y.ml-m
+m ~
(if
I >
(63
2)
I
where m,v,l are mass, velocity and track length o f the fragment, mp and m t are projectile and t a r F t mass, respectively. P~. is incident momentum. The coefficients C~, are determined by a calibration procedure which has been discussed in detail in referencesO'4}. We used the parameters of about 400 elastic two prongs events to calibrate the coefl'udents of C~. The values of C.v calibrated by this method are listed in Table 3. Table 3. Coefficients of C,, from elastic two prongs events Cur
v=0
v=l
v=2
v=3
v=4
u =, 0
1.134E-1
1.379E-2
2.848E-3
-2.124E-4
4.042E-6
u- 1
-1.380E-3
3.252E--4
-3.028E-5
1.082E-6
-1.411E-8
u=2
4.006E-6
-1.199E-6
1.049E-7
-3~221E-9
2.978E-11
This set of coefficients C,, were used to analyse the multifragment events. Table 4 lists the numbers of events which we measured. Table 4. Numbers of events treated in this work 3-prongs events
4-prongS events
5-prongs events
direct
107
50
4
indirect
57
55
1
total
164
105
5
measured(I)
98
38
--
analysed(2)
83
2.5
--
selected(3)
73
21
--
In our study we found that only a part of direct multiprongs events could be measured for obtaining their complete track lengths. Only about 1 / 3 of total events could be analysed by using the coefficients Cur and only a part of the analysed events could fit into the framework 1.9 ~ V , , ~ 3 . 1 cm / nsec, which is the characteristic velocity between two fragments in nuclear fission. The final fragment mass distribution of selected 3-prongs events are Gauss/an shape, integsrated over all enersies and angsles. Two fission fragments with m , = 9 5 + 33u and mr= 153 + 30u and one surv/ring fragment ink= 210 ± 40U are observed. Here one of the uranium nuclei, after experiencings a nuclear collision and handing over a net amount of mass to the other, survives fission. The compl~nentary particle fissions in the second step of the reaction and yields two typical f'm/on fraj. ments. The sum o f the correlated fission fragment masses (m i and mj)have an averafp; value o f 252± 32u, representing the mass of one intermediate nuclei which would undergo fission sequentially. The T K E L can be deduced, event by event, from the expression TKEL - E~
-- ( ~ E I - E t)
(7)
636
ZHOU PEI-DE
et aL
m,mlV ~ E r " 2(m, + m l )
(n
-
3)
(S)
(n > 3)
(9)
or
E-
F2 t I q.
m m
mtmiF'~
r 2(m, + ml7 + 2(m, + m,)
E, is the kinetic energy assoeiated to each track. The kinetic energy available above the entrance coulomb barrier (P..,,,,) is 955Mev in the present reaction. Some events which T K E L is hurj~ than have been observed experimentally. It shows that the effects ofdetormation and mass or charlie transfer of the intermediate fragments formed in the first reaction step must be taken into account for tome events. In order to study the sequential fission process further, for example, reamnable explanation concerning the relative high amount of three prong events in the reaction channel and higher energy damping, it is on the right way to examine the mass transfer in detail. According to the mass transfer distributions of selected 3-prong events in the three T K E L intervals, (a)-l$0 ~300Mev, (b)300,- 600Mev, (c)600-- 900Mev, we known that the mean mass tranffer in case of the deep inelastic collision is larger as compared to that in less damped reactions. The largest mass transfer with a mean value of 38± 18u has been observed for three prong events in the highest T K E L re,. gion.
If mass transfer is larger, one oftbe intermed/ate nuclei is too light or its intrinsic excitation energy is too low such that the probability to undergu rission is small and there/ore this intermed/ate mass survives, and this process yields three final masses. CONCLUSION The reaction cross sections determined with theoretical and experimental methods arc in good NFeement. We could say that the main react/on channel of the reaction in the incident energy studied is multifragment emission after collisions of the projectiles and target nuclei. According to quantitative analyses, most of the multifragment events are resulted form sequential fission after inelastic collision of" the projectiles and target nuclei. After inelastic collision, one or two uranium undergo fission to appear as 3-, 4 - or 5-prong events, respectively. The er3/ ~4 value and the higher mass transfer at h/ghest TKEL region shows a tend that when fully damp reaction occurred it is most probable to yieid 3 fmal masses and in high projectile energy the cross sect/on of fully damp reaction is qunt/tetively larger. It is my pleasure to thank Prof. Gun Shi-Lun for his guidance and Prof. Dr. R.Brandt and Dr. P.Vater, Marburg University for their kind cooperation. I am indebted to Dr. l.B.Qureshi for guilding the use of the program PRONOY and Dr. F.Hubert for providing the projram calaulating the stopping power and range. REFERENCES
1. Durrani, S.A. and Bull, R.K. (1957). Solid State Nuclear Track Detsction --Principics, Methods and Applicatons, England. 2. Khan, E.U~(1989). Ph.D. Thesis, Study of the heavy ion reaction =e13+~WUat the beam eaer~km of 9.0 and 16.7 Mev / N using mica as solid state nuclear track detector. 3. Khan, H.A. (1964-1989). Selected Research , .Publ/cat/onsofDrJ-I.A.Khan. 4. Gottschalk, P.A. and Grawer~ G. (1983). Physics Review, C27. 5. Vater, P. ~ al. (1977). Nuclear .Instrum.ent and Methods, 147. 6. Brandt, R. et al. (1980). Nuclear TnsU'llJm(~trand M(~,, o~., ~.73. 7. Bast, R. (1980). Nuclear Reaction s With fleavy Ions, Berlin. 8. Hubert, F. etal. (1990). R a n p and Stopping-Power Tables for 2 . 5 - $ 0 0 M e v / N Heavy Ions in Solids, Atomic Data and Nuclear Data Tabics, Vol.~_., N0.1.