- Email: [email protected]
Measuring system of proton total reaction cross-sections at tandem energy region
Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
Measuring system of proton total reaction cross-sections at tandem energy region N. Okumuraa,*, Y. Aokia, T. Joha, Y. Honkyua, K. Hirotab, K.S. Itohc a
Institute of Physics and Tandem Accelerator Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan b Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japan c Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japan Received 21 May 2001; received in revised form 27 November 2001; accepted 10 December 2001
Abstract Proton total reaction cross-sections of nat Si and nat Al have been measured by using a very simple attenuation technique. Energy range is 14–17 MeV; which covers the threshold energy of 28 Si(p,n). Features include well-defined beam and very low noise counters, elastic and inelastic scattering corrections. The energy dependence of total reaction cross-sections of nat Si shows a resonance-like behavior just above the 28 Si(p,n) threshold energy. r 2002 Elsevier Science B.V. All rights reserved. PACS: 29.40.Cs; 29.90.+r; 25.60.Dz Keywords: Proton total reaction cross-section; Attenuation method
1. Introduction Total reaction cross-section, sR ; describes the probability that the incident flux is lost from the elastic channel. It is used to extract nuclear radius RA by the following simple relation, sR ¼ pðRp þ RA Þ2 [1], where Rp is the radius of projectile. It is recognized that the nuclear radius RA is fairly constant for wide energy range and the energy dependence of sR is mainly determined by the energy dependence of the de Broglie wavelength of the relative motion. Total reaction cross-section is suppressed appreciably for charged particles by the Coulomb interaction when incident energy is below the Coulomb barrier. *Corresponding author. E-mail address: [email protected] (N. Okumura).
Sometimes sR is used to restrict optical potential parameters, because expectation value of the imaginary potential is proportional to sR : Based on the dispersion relation, the imaginary potential is related to the real potential; the information of sR is a very important parameter for the optical model. Apart from the macroscopic or geometric views, the total reaction cross-section may reveal some microscopic structure of the target nucleus. The optical model potential, VOpt ; may be expressed as follows [2]: VOpt ¼ VPP þ VPQ
1 VQP : E HQQ þ ie
ð1Þ
The imaginary potential comes from the second term on the right-hand side. A resonance-like energy dependence of sR should be expected when
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 2 2 0 1 - X
566
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
the Green’s function changes sign and the matrix elements of VQP and VPQ are very large. If we neglect the non-orthogonality effects, the closed (p,n) channel term should destructively interfere with that of the open ðp; p0 Þ channel and interfere constructively when the incident energy is increased and the (p,n) channel is opened: This resonance-like energy dependence may be observed as a threshold effect of the (p,n) reaction in the proton-28 Si total reaction cross-section at around 16 MeV: With this scenario in mind, a measurement of the energy dependence of the proton total reaction cross-section is carried out for nat Si at Ep ¼ 14–17 MeV: A few methods are reported to measure total reaction cross-sections. The total reaction crosssection can be evaluated by summing the integrated cross-sections of all inelastic channels [3]. Some authors extracted total reaction crosssections by assuming that the low-energy tail of elastic peak is due to the nuclear reactions in the detector [4]. This method is limited to the nuclei which are used as detectors. Gooding [5] assumed that the incident particle is absorbed or scattered away whenever nuclear reaction is induced in the target, i.e., I ¼ expðnxsR Þ or I0
sR ¼
1 I0 I nx I0
should correctly be taken into account to extract the real total reaction cross-sections. Dicello and Igo [7] used a detector assembly, which stacked a small thin plastic scintillator and a thick solid state detector, to overcome this difficulty. All the particles that fired the thin scintillator were counted as non-reaction events. The thick counter has enough energy resolution to discriminate elastic from non-elastic events. We did not use this approach, because the light collection efficiency of the thin plastic scintillator is not good and because of the difficulties in setting the discrimination level of elastic tail of the solid state detector. As is stated in (1), nuclear reaction events in the detector are much more frequent than in the target. Energy dependence of sR of the target may be obscured by that of reactions in the detector. (3) There is a small but finite probability of compound elastic scattering, where the absorbed flux reappears in the elastic channel. Compound elastic process may safely be neglected, when the level density is high and the branching ratio to the elastic channel is very small. The experimental method is described in the next section. The results and discussions including elastic and inelastic corrections are given in the last section.
ð2Þ
where n is the number density and x is the thickness of the target and I0 (I) is the number of projectiles which hit (passed through) the target. This beam attenuation method was successfully used by many authors [6]. Simplicity is the virtue of this attenuation method, while the following points should be noted. (1) The accuracy is mainly limited by the difference I0 I; which is usually o103 of I0 or I: All the efforts should be made not to allow ambiguous events to leak into the I0 and I counters. Unclear events may be introduced, for example, by beam halos, nuclear reactions in the counter, inefficiency of counters and insufficient time resolution. (2) Elastic events into backward angles that failed to hit the I counter and the non-elastic events into forward angles that fired the I counter
2. Experimental A Pelletron-type electrostatic tandem accelerator at the University of Tsukuba was used. A plan view of the beam transport system is shown in Fig. 1. Energy stabilizing system of this accelerator requires 1 nA of accelerated beam to hit the highand/or low-energy slit jaw of the momentumanalyzing magnet. The beam intensity should be reduced by about a factor of 106 in transporting from a momentum-analyzing magnet to the target. This reduction factor is mainly realized by using a round slit (b) and by not activating the quadrupole magnets. Four high-sensitivity beam current integrators, which consist of a buffer amplifier and a voltage-to-frequency converter, were used to measure the beam current on the jaws of the slit (d) and to center the beam path. Every effort was made to reduce beam halos and slit edge
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
567
Fig. 1. Plan view of the beam transport system. The label (a) denotes image slit of the momentum-analyzing magnet. Beam-collimating slits are labeled (b)–(d). Details of the region enclosed by dashed lines are given in Fig. 2. Distances are given in mm.
scattering. Two active slits, each of which consists of a plastic scintillator coupled with a photomultiplier tube, are used to veto the unclear events. Fig. 2 shows the configuration of the counter and target assembly. The number of protons which hit the target, I0 ; was counted by using a pair of proportional counters. The anode of these counters is 15 mm thick gold-coated tungsten wire. The anode wires are placed at 1:5 mm from the beam center, lest they are hit by incident protons. The counter gas is a mixture of CH4 (30 vol%) and Ar (70 vol%) and the operating pressure was 0:5 atom: The total thickness of this I0 counter system is 3:8 mg=cm2 ; or 100 keV for 15 MeV protons. Typical spectra of the proportional counter and I counter are given in Fig. 3. The gas gain is high enough to reject any background or noise from the true events. The coincidence efficiency of the two counters for protons amounts to > 99:99%; i.e., virtually no protons are lost in this pair of proportional counters. This good signal-to-noise ratio can never be realized by using thin plastic scintillators. Dicello et al. [8] used two thin plastic scintillators, which are separated by two inches, and reported that the coincidence efficiency of these detectors was about 25%. Targets were polished nat Si of 50 and 100 mm thickness. The energy loss of 15 MeV protons for nat Si ð100 mm thick) is about 600 keV: nat Al foil of 100 mm thickness was used to confirm the consistency of these measurements with the numerical values of sR reported by Pollock and Schrank [9].
Fig. 2. Schematic diagram of detectors and target arrangement. Counters (1) and (4) are active slits. The proportional counters are labeled (2) and (3). Counter (5) denotes the I counter. The horizontal dimension is shown by a ruler.
The energy dependency of sR for nat Si was compared with that for nat Al. The Q-value of 27 Al(p,n) reaction is 5:59 MeV: The number of protons which passed through the target was counted by a round 100 mm thick plastic scintillator pasted onto a 1:5 in: photomultiplier tube. The aperture angle of this counter is 511: More than 99.97% of protons which passed through the I0 counters are detected when a ‘blank’ target was used. The ratio of I=I0 is reduced to 99.8% when this plastic scintillator was replaced by a solid state detector. Low-noise character of the counters in Fig. 3 implies that the discrimination problem in counting electronics is trivial.
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570 105
10
6
4
10
5
10 10
3
10
2
10
1
10
0
104
Counts
Counts
568
10
3
102 101
0
200
400
600
800
10
1000
Channel No.
0
0
200
400
600
800
1000
Channel No.
(a)
(b)
Fig. 3. Single spectra of I0 (panel a) and I (panel b) counters when 15 MeV protons were detected. The main peak area in the I0 counter spectrum is about 1:2 106 counts while the area below channel 80 is zero. The area from channel 100 to 180 is about 0.03% of that from channel 100 to 1000 for the I counter spectrum. The arrows show the threshold levels: (a) Spectrum of proportional counter; (b) Spectrum of I counter.
Fig. 4. Circuit diagram of a proportional counter. SA and TSCA mean spectroscopic amplifier and timing single-channel analyzer, respectively. Time relation of coincidence and anti-coincidence signals at (A) and (B) is given in the inset. The logic signal (C) is fed into coincidence circuit of Fig. 5.
Fig. 4 shows the block diagram to handle analog signals from a proportional counter. A dead time of 5 ms was introduced after the I0 counter fired. This dead time is long enough to adjust the difference of time response of a set of proportional counters and a plastic scintillator. Counting rate was adjusted to be 1 kHz: Counting efficiency was a little degraded and about 10% increase of sR is estimated when the counting rate is increased over 2 kHz: Counting logic of I0 and I is illustrated in Fig. 5. As is shown in Fig. 5, pulses from active slits, proportional and I counters are denoted as (1), (4), (2), (3) and (5), respectively. I0 and I in Eq. (2) are defined by the following coincidence/ anti-coincidence relation: I0 ¼ ð1Þð2Þð3Þð4Þ
and
I ¼ ð1Þð2Þð3Þð4Þð5Þ:
ð3Þ
About 0.1% and 0.03% of pulses from the proportional counters are blocked by pulses from active slits (1) and (4), respectively. Four targets, nat Si of 50 and 100 mm thick, aluminum of 100 mm thick and ‘blank’, were used interchangeably.
3. Results and discussion Raw total reaction cross-section sraw was R evaluated by the following expression: 1 I0 I i0 i ¼ sraw ð4Þ R nx I0 i0 where i0 and i stand for I0 and I for blank target, respectively. Blank target correction was generally
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
569
Active slit (1) Proportional counter (2)
Anti-coin. Coin. Coin.
Coincidence
Proportional counter (3)
Scalar
0
Anti-coin.
(1)(2)(3)(4)
Active slit (4) Coin.
I counter (5)
Coin.
Coincidence
Scalar (1)(2)(3)(4)(5)
Fig. 5. Counting logic of I0 and I: Time width of the logic pulse is about 2 ms:
750
R
raw
[mb]
700
Si
Table 1 Energy dependence of sraw R for
Al
Ep (MeV)
nat
600
550 13.5
14
14.5
15
15.5 16 Ep [MeV]
16.5
17
17.5
Si and
nat
Al and sR for
sraw R (mb)
Ref. [9]
650
nat
14.0 15.0 15.5 15.75 16.0 16.25 16.5 17.0
Si
589 620 643 618 591 690 630 621
nat
Si
sR (mb) nat
Al
636 661 680 684
nat
Si
741 772 804 770 752 880 830 813
Fig. 6. Energy dependence of proton total reaction crosssections, sraw R : Error bars of filled point are due to statistics.
amounted to 20–25% of sraw R : Fig. 6 shows the incident energy dependence of sraw of nat Si and R nat Al. As was expected, a resonance-like behavior was observed for nat Si target, while smooth energy dependence was seen for nat Al target. After a year, some of the typical data points were confirmed to be reproducible. A data point shown by open circle is taken from Ref. [9]. Elastic and inelastic corrections for nat Si were made as follows. We already observed crosssections sðyÞ and vector-analyzing powers to the ground and to the first excited ðEx ¼ 1:78 MeVÞ states in 28 Si at 8 energy points from Ep ¼ 13:9 to 17:5 MeV [10]. The quality of the data for inelastic scattering, however, was not good because of the poor statistics. The coupled channels code
CHUCK2 [11], where an automatic fitting function of experimental observables was added, was used to reproduce these cross-sections and vectoranalyzing power data. The total reaction crosssections, sR ; was calculated by the following expression: sR ¼ sraw R þ
Z
sinel ðyÞ dO O
Z % O
sel ðyÞ dO
ð5Þ
where sel and sinel are calculated elastic and inelastic cross-sections, respectively. The integration range O refers to the solid angle subtended by % is the complement of O: We the I counter and O noticed that the angular acceptance of I counter was set so that large cancelation among elastic and inelastic corrections took place. The corrected reaction cross-sections, sR ; are given in Table 1.
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N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
4. Conclusion The energy dependence of the total reaction cross-section of the p þnat Si system was measured by using very thin proton counters. Elastic correction was made. Inelastic corrections which lead to the first excited state were also made with some uncertainty of about 10 mb: As was expected, resonance-like behavior of sR in p+Si system was found. The width of the resonance-like behavior is about 300 keV; which corresponds to 2 1021 s of time delay. No correction was made for p+Al case, but the present figure is fairly consistent with the one in Ref. [9]. It is expected that by combining this energy dependence of sR with the detailed behavior of elastic scattering data one can infer the reaction mechanism.
References [1] R.F. Carlson, Atom. Data Nucl. Data Tables 63 (1996) 93.
[2] N.K. Glendenning, Direct Nuclear Reactions, Academic Press, New York, 1983 (Chapter 8). [3] A. Budzanowski, L. Freindl, K. Grotowski, M. Rzeszutko, M. Slapa, J. Szmider, P.E. Hodgson, Nucl. Phys. 49 (1963) 144. [4] M.Q. Makino, C.N. Waddell, R.M. Eisberg, Nucl. Instr. and Meth. 60 (1968) 109; R.F. Carlson, A.J. Cox, N.E. Davison, R.H. McCamis, Nucl. Instr. and Meth. A 236 (1985) 100. [5] T.J. Gooding, Nucl. Phys. 12 (1959) 241. [6] A. Ingemarsson, J. Nyberg, P.U. Renberg, O. Sundberg, R.F. Carlson, A. Auce, R. Johansson, G. Tibell, B.C. Clark, L. Kurth Kerr, S. Hama, Nucl. Phys. A 653 (1999) 341 and the references therein. [7] J.F. Dicello, G. Igo, Phys. Rev. C 2 (1970) 488. [8] J.F. Dicello, G.J. Igo, M.L. Roush, Phys. Rev. 157 (1967) 1001. [9] R.E. Pollock, G. Schrank, Phys. Rev. 140 (1965) B575. [10] K. Hirota, K. Miura, K. Koyama, N. Okumura, H. Kishita, Y. Mukouhara, S. Nakagawa, M. Masaki, Y. Tagishi, Y. Aoki, UTTAC Annual Report, UTTAC-62, 1995, p. 13. [11] P.D. Kuntz, computer code CHUCK2, private communications.
Measuring system of proton total reaction cross-sections at tandem energy region N. Okumuraa,*, Y. Aokia, T. Joha, Y. Honkyua, K. Hirotab, K.S. Itohc a
Institute of Physics and Tandem Accelerator Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan b Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japan c Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japan Received 21 May 2001; received in revised form 27 November 2001; accepted 10 December 2001
Abstract Proton total reaction cross-sections of nat Si and nat Al have been measured by using a very simple attenuation technique. Energy range is 14–17 MeV; which covers the threshold energy of 28 Si(p,n). Features include well-defined beam and very low noise counters, elastic and inelastic scattering corrections. The energy dependence of total reaction cross-sections of nat Si shows a resonance-like behavior just above the 28 Si(p,n) threshold energy. r 2002 Elsevier Science B.V. All rights reserved. PACS: 29.40.Cs; 29.90.+r; 25.60.Dz Keywords: Proton total reaction cross-section; Attenuation method
1. Introduction Total reaction cross-section, sR ; describes the probability that the incident flux is lost from the elastic channel. It is used to extract nuclear radius RA by the following simple relation, sR ¼ pðRp þ RA Þ2 [1], where Rp is the radius of projectile. It is recognized that the nuclear radius RA is fairly constant for wide energy range and the energy dependence of sR is mainly determined by the energy dependence of the de Broglie wavelength of the relative motion. Total reaction cross-section is suppressed appreciably for charged particles by the Coulomb interaction when incident energy is below the Coulomb barrier. *Corresponding author. E-mail address: [email protected] (N. Okumura).
Sometimes sR is used to restrict optical potential parameters, because expectation value of the imaginary potential is proportional to sR : Based on the dispersion relation, the imaginary potential is related to the real potential; the information of sR is a very important parameter for the optical model. Apart from the macroscopic or geometric views, the total reaction cross-section may reveal some microscopic structure of the target nucleus. The optical model potential, VOpt ; may be expressed as follows [2]: VOpt ¼ VPP þ VPQ
1 VQP : E HQQ þ ie
ð1Þ
The imaginary potential comes from the second term on the right-hand side. A resonance-like energy dependence of sR should be expected when
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 2 2 0 1 - X
566
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
the Green’s function changes sign and the matrix elements of VQP and VPQ are very large. If we neglect the non-orthogonality effects, the closed (p,n) channel term should destructively interfere with that of the open ðp; p0 Þ channel and interfere constructively when the incident energy is increased and the (p,n) channel is opened: This resonance-like energy dependence may be observed as a threshold effect of the (p,n) reaction in the proton-28 Si total reaction cross-section at around 16 MeV: With this scenario in mind, a measurement of the energy dependence of the proton total reaction cross-section is carried out for nat Si at Ep ¼ 14–17 MeV: A few methods are reported to measure total reaction cross-sections. The total reaction crosssection can be evaluated by summing the integrated cross-sections of all inelastic channels [3]. Some authors extracted total reaction crosssections by assuming that the low-energy tail of elastic peak is due to the nuclear reactions in the detector [4]. This method is limited to the nuclei which are used as detectors. Gooding [5] assumed that the incident particle is absorbed or scattered away whenever nuclear reaction is induced in the target, i.e., I ¼ expðnxsR Þ or I0
sR ¼
1 I0 I nx I0
should correctly be taken into account to extract the real total reaction cross-sections. Dicello and Igo [7] used a detector assembly, which stacked a small thin plastic scintillator and a thick solid state detector, to overcome this difficulty. All the particles that fired the thin scintillator were counted as non-reaction events. The thick counter has enough energy resolution to discriminate elastic from non-elastic events. We did not use this approach, because the light collection efficiency of the thin plastic scintillator is not good and because of the difficulties in setting the discrimination level of elastic tail of the solid state detector. As is stated in (1), nuclear reaction events in the detector are much more frequent than in the target. Energy dependence of sR of the target may be obscured by that of reactions in the detector. (3) There is a small but finite probability of compound elastic scattering, where the absorbed flux reappears in the elastic channel. Compound elastic process may safely be neglected, when the level density is high and the branching ratio to the elastic channel is very small. The experimental method is described in the next section. The results and discussions including elastic and inelastic corrections are given in the last section.
ð2Þ
where n is the number density and x is the thickness of the target and I0 (I) is the number of projectiles which hit (passed through) the target. This beam attenuation method was successfully used by many authors [6]. Simplicity is the virtue of this attenuation method, while the following points should be noted. (1) The accuracy is mainly limited by the difference I0 I; which is usually o103 of I0 or I: All the efforts should be made not to allow ambiguous events to leak into the I0 and I counters. Unclear events may be introduced, for example, by beam halos, nuclear reactions in the counter, inefficiency of counters and insufficient time resolution. (2) Elastic events into backward angles that failed to hit the I counter and the non-elastic events into forward angles that fired the I counter
2. Experimental A Pelletron-type electrostatic tandem accelerator at the University of Tsukuba was used. A plan view of the beam transport system is shown in Fig. 1. Energy stabilizing system of this accelerator requires 1 nA of accelerated beam to hit the highand/or low-energy slit jaw of the momentumanalyzing magnet. The beam intensity should be reduced by about a factor of 106 in transporting from a momentum-analyzing magnet to the target. This reduction factor is mainly realized by using a round slit (b) and by not activating the quadrupole magnets. Four high-sensitivity beam current integrators, which consist of a buffer amplifier and a voltage-to-frequency converter, were used to measure the beam current on the jaws of the slit (d) and to center the beam path. Every effort was made to reduce beam halos and slit edge
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
567
Fig. 1. Plan view of the beam transport system. The label (a) denotes image slit of the momentum-analyzing magnet. Beam-collimating slits are labeled (b)–(d). Details of the region enclosed by dashed lines are given in Fig. 2. Distances are given in mm.
scattering. Two active slits, each of which consists of a plastic scintillator coupled with a photomultiplier tube, are used to veto the unclear events. Fig. 2 shows the configuration of the counter and target assembly. The number of protons which hit the target, I0 ; was counted by using a pair of proportional counters. The anode of these counters is 15 mm thick gold-coated tungsten wire. The anode wires are placed at 1:5 mm from the beam center, lest they are hit by incident protons. The counter gas is a mixture of CH4 (30 vol%) and Ar (70 vol%) and the operating pressure was 0:5 atom: The total thickness of this I0 counter system is 3:8 mg=cm2 ; or 100 keV for 15 MeV protons. Typical spectra of the proportional counter and I counter are given in Fig. 3. The gas gain is high enough to reject any background or noise from the true events. The coincidence efficiency of the two counters for protons amounts to > 99:99%; i.e., virtually no protons are lost in this pair of proportional counters. This good signal-to-noise ratio can never be realized by using thin plastic scintillators. Dicello et al. [8] used two thin plastic scintillators, which are separated by two inches, and reported that the coincidence efficiency of these detectors was about 25%. Targets were polished nat Si of 50 and 100 mm thickness. The energy loss of 15 MeV protons for nat Si ð100 mm thick) is about 600 keV: nat Al foil of 100 mm thickness was used to confirm the consistency of these measurements with the numerical values of sR reported by Pollock and Schrank [9].
Fig. 2. Schematic diagram of detectors and target arrangement. Counters (1) and (4) are active slits. The proportional counters are labeled (2) and (3). Counter (5) denotes the I counter. The horizontal dimension is shown by a ruler.
The energy dependency of sR for nat Si was compared with that for nat Al. The Q-value of 27 Al(p,n) reaction is 5:59 MeV: The number of protons which passed through the target was counted by a round 100 mm thick plastic scintillator pasted onto a 1:5 in: photomultiplier tube. The aperture angle of this counter is 511: More than 99.97% of protons which passed through the I0 counters are detected when a ‘blank’ target was used. The ratio of I=I0 is reduced to 99.8% when this plastic scintillator was replaced by a solid state detector. Low-noise character of the counters in Fig. 3 implies that the discrimination problem in counting electronics is trivial.
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570 105
10
6
4
10
5
10 10
3
10
2
10
1
10
0
104
Counts
Counts
568
10
3
102 101
0
200
400
600
800
10
1000
Channel No.
0
0
200
400
600
800
1000
Channel No.
(a)
(b)
Fig. 3. Single spectra of I0 (panel a) and I (panel b) counters when 15 MeV protons were detected. The main peak area in the I0 counter spectrum is about 1:2 106 counts while the area below channel 80 is zero. The area from channel 100 to 180 is about 0.03% of that from channel 100 to 1000 for the I counter spectrum. The arrows show the threshold levels: (a) Spectrum of proportional counter; (b) Spectrum of I counter.
Fig. 4. Circuit diagram of a proportional counter. SA and TSCA mean spectroscopic amplifier and timing single-channel analyzer, respectively. Time relation of coincidence and anti-coincidence signals at (A) and (B) is given in the inset. The logic signal (C) is fed into coincidence circuit of Fig. 5.
Fig. 4 shows the block diagram to handle analog signals from a proportional counter. A dead time of 5 ms was introduced after the I0 counter fired. This dead time is long enough to adjust the difference of time response of a set of proportional counters and a plastic scintillator. Counting rate was adjusted to be 1 kHz: Counting efficiency was a little degraded and about 10% increase of sR is estimated when the counting rate is increased over 2 kHz: Counting logic of I0 and I is illustrated in Fig. 5. As is shown in Fig. 5, pulses from active slits, proportional and I counters are denoted as (1), (4), (2), (3) and (5), respectively. I0 and I in Eq. (2) are defined by the following coincidence/ anti-coincidence relation: I0 ¼ ð1Þð2Þð3Þð4Þ
and
I ¼ ð1Þð2Þð3Þð4Þð5Þ:
ð3Þ
About 0.1% and 0.03% of pulses from the proportional counters are blocked by pulses from active slits (1) and (4), respectively. Four targets, nat Si of 50 and 100 mm thick, aluminum of 100 mm thick and ‘blank’, were used interchangeably.
3. Results and discussion Raw total reaction cross-section sraw was R evaluated by the following expression: 1 I0 I i0 i ¼ sraw ð4Þ R nx I0 i0 where i0 and i stand for I0 and I for blank target, respectively. Blank target correction was generally
N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
569
Active slit (1) Proportional counter (2)
Anti-coin. Coin. Coin.
Coincidence
Proportional counter (3)
Scalar
0
Anti-coin.
(1)(2)(3)(4)
Active slit (4) Coin.
I counter (5)
Coin.
Coincidence
Scalar (1)(2)(3)(4)(5)
Fig. 5. Counting logic of I0 and I: Time width of the logic pulse is about 2 ms:
750
R
raw
[mb]
700
Si
Table 1 Energy dependence of sraw R for
Al
Ep (MeV)
nat
600
550 13.5
14
14.5
15
15.5 16 Ep [MeV]
16.5
17
17.5
Si and
nat
Al and sR for
sraw R (mb)
Ref. [9]
650
nat
14.0 15.0 15.5 15.75 16.0 16.25 16.5 17.0
Si
589 620 643 618 591 690 630 621
nat
Si
sR (mb) nat
Al
636 661 680 684
nat
Si
741 772 804 770 752 880 830 813
Fig. 6. Energy dependence of proton total reaction crosssections, sraw R : Error bars of filled point are due to statistics.
amounted to 20–25% of sraw R : Fig. 6 shows the incident energy dependence of sraw of nat Si and R nat Al. As was expected, a resonance-like behavior was observed for nat Si target, while smooth energy dependence was seen for nat Al target. After a year, some of the typical data points were confirmed to be reproducible. A data point shown by open circle is taken from Ref. [9]. Elastic and inelastic corrections for nat Si were made as follows. We already observed crosssections sðyÞ and vector-analyzing powers to the ground and to the first excited ðEx ¼ 1:78 MeVÞ states in 28 Si at 8 energy points from Ep ¼ 13:9 to 17:5 MeV [10]. The quality of the data for inelastic scattering, however, was not good because of the poor statistics. The coupled channels code
CHUCK2 [11], where an automatic fitting function of experimental observables was added, was used to reproduce these cross-sections and vectoranalyzing power data. The total reaction crosssections, sR ; was calculated by the following expression: sR ¼ sraw R þ
Z
sinel ðyÞ dO O
Z % O
sel ðyÞ dO
ð5Þ
where sel and sinel are calculated elastic and inelastic cross-sections, respectively. The integration range O refers to the solid angle subtended by % is the complement of O: We the I counter and O noticed that the angular acceptance of I counter was set so that large cancelation among elastic and inelastic corrections took place. The corrected reaction cross-sections, sR ; are given in Table 1.
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N. Okumura et al. / Nuclear Instruments and Methods in Physics Research A 487 (2002) 565–570
4. Conclusion The energy dependence of the total reaction cross-section of the p þnat Si system was measured by using very thin proton counters. Elastic correction was made. Inelastic corrections which lead to the first excited state were also made with some uncertainty of about 10 mb: As was expected, resonance-like behavior of sR in p+Si system was found. The width of the resonance-like behavior is about 300 keV; which corresponds to 2 1021 s of time delay. No correction was made for p+Al case, but the present figure is fairly consistent with the one in Ref. [9]. It is expected that by combining this energy dependence of sR with the detailed behavior of elastic scattering data one can infer the reaction mechanism.
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