Radiation Measurements 33 (2001) 193–202www.elsevier.com/locate/radmeas

Energy loss of heavy ions in gases: a comparative study

P.K. Diwana, Shyam Kumarb; ∗, Gurinder Singha, Lakhwant SinghaaDepartment of Physics, Guru Nanak Dev University, Amritsar 143 005, IndiabDepartment of Physics, Kurukshetra University, Kurukshetra 136 119, India

Received 26 January 2000; accepted 16 August 2000

Abstract

A comparative study of various energy loss formulations has been made using the calculated stopping power values and thecorresponding experimental values for projectile ions with 86 Z6 92 in 11 gaseous media: the �ve monatomic rare gases(He to Xe), two diatomic gases (H2; N2) and four polyatomic compounds (CH4; C4H10; CO2 and CF4), in an energy range of∼ 1–80 MeV=n. The merits and demerits of the adopted formulations are highlighted. It has been observed that the calculationsbased on SRIM-2000.38 recently developed by Ziegler provides best agreement with the experimental results for projectileions with 86 Z6 47 in all these absorbers except the H2 gas absorber. c© 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction

Passage of heavy ions through matter and evaluation ofassociated energy loss have widespread and well-knownapplications in diverse disciplines (Ahlen, 1980). The stop-ping power for heavy ion in gases is of paramount impor-tance in nuclear reaction studies for the identi�cation ofreaction products using �E−E telescope detectors (Kapoorand Ramamurthy, 1986). In the absence of analytical ex-pressions for the two basic input parameters for stoppingpower calculations, viz. the e�ective charge of the ion asa function of ion speed and the mean ionization potentialof the target, the various energy loss formulations employempirical=semi-empirical relations to determine these twoparameters. The accuracy for estimating stopping powertherefore depends on the quality of �tness employed toworkout these expressions. However, there is a continuousneed to check the reliability of such formulations throughcomparison with the available experimental data. There arereports, which indicate that the experimental stopping powervalues for heavy ions in solids deviate signi�cantly from theoften-used semi-empirical models (Sharma et al., 1995a, b,Kumar et al., 1997; Randhawa and Virk, 1996).

∗ Corresponding author. Tel.: +91-1744-20410; fax:+91-1744-20277.E-mail address: kuru@doe.ernet.in (S. Kumar).

Regarding the stopping power for heavy ions in gaseousmedia, only a few reports are available (Bimbot et al., 1989a,b, 1996; Herault et al., 1991; Pierce and Blann, 1968). In thispaper, we have made an attempt to establish the validity ofvarious stopping power formulations for gaseous absorbersthrough comparison with the available experimental data.Further, such a study is important in order to identify thevariation in stopping power with the physical state of theabsorber. Such variation is reported to be due to the higherionic charge of the moving ion in solids relative to gaseousmedia (Bimbot et al., 1989b; Geissel et al., 1982, 1983).

2. Present work

In the present work, a comparative study of di�erent stop-ping power formulations, e.g. Benton and Henke (1969),Northcli�e and Schilling (1970), Mukherjee and Nayak(1979), Ziegler et al. (1985), Ziegler (1999) and Hubert etal. (1989), have been made using the respective calculatedstopping power values vis-a-vis the available experimentalstopping power values. The Northcli�e and Schilling tabu-lated stopping power values are available up to 12 MeV=nin a limited number of absorbers only. The computer codeSRIM-2000.38 recently developed by Ziegler is used forstopping power calculations from Ziegler et al. (1985,1999) formulation. The experimental stopping power dataof Bimbot et al. (1989a, b, 1996), Herault et al. (1991) and

1350-4487/01/$ - see front matter c© 2001 Elsevier Science Ltd. All rights reserved.PII: S1350 -4487(00)00144 -X

194 P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202

Table 1Experimental and calculated stopping power values for Ne, S, Cl, Ar, Cu and Kr projectiles in di�erent gaseous targets at energies∼ 1–3 MeV=na

Energy Projectile Gas Sexpb SRIM-2000.38 Benton and Mukherjee Northcli�e(MeV=n) target (MeV=mg cm−2) Henke and Nayak and Schilling

2:98 Ne H2 24:9± 1:3 22:0(−12) 24:2(−3) 24:1(−3) 23:9(−4)2:88 Ne He 11:3± 0:5 10:6(−6) 10:5(−7) — 10:8(−4)3:01 Ne He 11:1± 0:6 10:3(−7) 10:3(−7) — 10:5(−5)2:37 Ne N2 9:1± 0:2 9:1(0) 9:4(3) 8:7(−4) 9:1(0)2:74 Ne N2 8:5± 0:2 8:5(0) 8:8(3) 8:3(−2) 8:6(1)2:47 Ne Ne 7:7± 0:2 7:8(1) 8:2(6) 7:7(0) 7:8(1)2:69 Ne Ne 7:5± 0:2 7:5(0) 7:9(5) 7:5(0) 7:6(1)2:20 Ne Ar 6:4± 0:2 6:4(0) 6:5(1) 6:2(−3) 6:4(0)2:73 Ne Ar 6:0± 0:2 5:9(−2) 6:0(0) 5:8(−3) 6:0(0)2:28 Ne Kr 4:8± 0:15 4:9(2) 4:8(0) 4:6(−4) 4:7(−2)2:88 Ne Kr 4:5± 0:2 4:4(−2) 4:4(−2) 4:4(−2) 4:4(−2)2:24 Ne Xe 4:1± 0:1 4:1(0) 3:9(−5) 3:8(−7) 3:9(−5)2:63 Ne Xe 3:9± 0:1 3:9(0) 3:7(−5) 3:7(−5) 3:8(−2)1:49 S H2 72:0 59:4(−17) 68:1(−5) 64:5(−10) 72:9(4)2:75 S H2 54:0 46:8(−13) 54:7(1) 53:5(−1) 49:8(−8)1:50 S He 28:5 28:3(−1) 27:2(−4) — 28:1(−1)2:08 S He 25:8 24:9(−3) 25:1(−3) — 24:8(−4)2:17 S N2 18:1 18:7(3) 19:7(9) 16:6(−8) 18:2(1)2:77 S N2 16:8 17:2(2) 18:3(9) 16:7(−1) 16:7(−1)1:39 S Ar 13:3 14:2(7) 13:7(3) 11:9(−10) 13:2(−1)2:05 S Ar 12:5 12:9(3) 13:1(5) 12:0(−4) 12:4(−1)2:06 S Kr 9:1 9:9(9) 9:5(4) 8:8(−3) 9:1(0)2:53 S Kr 9:0 9:3(3) 9:2(2) 8:7(−3) 8:9(−1)1:92 Cl H2 72:0 59:2(−18) 68:9(−4) 66:3(−8) 68:2(−5)2:40 Cl H2 63:0 54:2(−14) 63:6(1) 61:9(−2) 58:9(−6)1:09 Cl He 32:4 33:3(3) 30:4(−6) — 32:7(1)1:62 Cl He 31:7 29:9(−6) 28:9(−9) — 29:4(−7)2:55 Cl He 25:8 24:9(−3) 25:7(0) — 24:3(−6)1:52 Cl N2 21:4 22:4(5) 22:7(6) 19:9(−7) 21:6(1)2:30 Cl N2 19:3 20:1(4) 21:1(9) 17:3(−10) 19:3(0)1:41 Cl Ar 14:0 15:4(10) 14:7(5) 12:8(−8) 14:2(1)2:54 Cl Ar 12:8 13:3(4) 13:6(6) 12:7(−1) 12:9(1)2:11 Ar H2 77:0± 3 60:6(−21) 72(−6) 70(−9) 69(−10)2:27 Ar H2 73:0± 6 59:1(−19) 70(−4) 69(−5) 66(−9)2:08 Ar He 31:0± 1 28:8(−7) 30(−3) — 29(−6)2:26 Ar He 29:0± 2 28:0(−3) 29(0) — 28(−3)1:71 Ar N2 23:2± 0:9 22:9(−1) 24:1(4) 20:6(−11) 22:6(−2)2:08 Ar N2 21:8± 0:9 21:9(0) 23:3(7) 19:2(−12) 21:4(−2)1:78 Ar Ne 20:8± 0:8 19:6(−6) 20:9(0) 18:8(−10) 19:2(8)2:19 Ar Ne 18:7± 0:9 18:8(0) 20:2(8) 18:4(−2) 18:3(−2)1:76 Ar Ar 15:3± 0:6 15:4(1) 15:5(1) 14:0(−8) 14:7(−4)3:00 Ar Ar 14:0± 0:5 13:7(−2) 14:2(1) 13:3(−5) 13:5(−3)2:09 Ar Kr 11:2± 0:5 11:4(2) 11:1(−1) 10:2(−9) 10:6(−5)1:93 Ar Xe 10:1± 0:4 9:6(−5) 8:9(−12) 8:1(−20) 8:7(−14)2:04 Ar Xe 10:0± 0:5 9:6(−4) 8:9(−11) 8:2(−18) 8:7(−13)1:95 Cu H2 135:0± 8 115:7(−14) 136:9(1) 134:6(0) 124:9(−7)2:00 Cu H2 137:0± 1 115:1(−16) 136:5(0) 134:7(−2) 123:4(−10)2:56 Cu He 52:0± 2 51:0(−2) 52:9(2) — 46:6(−10)2:82 Cu He 49:0± 3 49:4(1) 52:1(6) — 45:0(−8)2:03 Cu N2 42:0± 2 41:3(−2) 41:9(0) 38:8(−8) 37:4(−11)1:81 Cu Ne 35:4± 1:5 36:1(2) 36:3(2) 33:4(−6) 32:6(−8)2:04 Cu Ne 34:0± 3 35:8(5) 36:4(7) 34:1(0) 32:2(−5)1:85 Cu Ar 26:0± 1 28:4(9) 26:7(3) 24:9(−4) 25:4(−2)2:13 Cu Ar 26:0± 2 28:0(8) 26:8(3) 25:6(−1) 25:0(−4)1:62 Cu Kr 18:4± 0:7 21:6(17) 18:9(3) 17:0(−8) 18:0(−2)

P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202 195

Table 1 (continued)

Energy Projectile Gas Sexpb SRIM-2000.38 Benton and Mukherjee Northcli�e(MeV=n) target (MeV=mg cm−2) Henke and Nayak and Schilling

1:90 Cu Kr 18:4± 0:9 21:6(17) 19:2(4) 17:8(−3) 18:2(−1)1:72 Cu Xe 17:4± 0:6 17:9(3) 15:1(−13) 13:9(−20) 14:8(−15)2:01 Cu Xe 17:6± 0:8 17:9(2) 15:4(−12) 14:6(−17) 15:0(−15)1:82 Kr H2 193:0± 8 143:6(−25) 174:1(−10) 171:6(−11) 162(−16)3:05 Kr H2 164:0± 7 130:9(−20) 166:9(2) 169:1(3) 127(−22)1:98 Kr He 73:0± 2 67:3(−8) 68:4(−6) — 64(−12)2:93 Kr He 67:0± 3 62:1(−7) 67:5(1) — 57(−15)1:95 Kr N2 53:0± 2 51:1(−3) 52:4(−1) 49:0(−7) 47(−11)2:85 Kr N2 49:0± 2 49:2(0) 52:7(7) 50:9(4) 45(−8)2:65 Kr Ne 43:9± 1:5 43:3(−1) 46:0(5) 45:1(3) 39:8(−9)3:00 Kr Ne 42:6± 1:5 42:7(0) 45:9(8) 45:2(6) 39:0(−8)2:05 Kr Ar 33:0± 1 34:6(5) 33:4(1) 32:6(−1) 31(−6)2:19 Kr Ar 32:5± 1:5 34:5(6) 33:6(3) 32:9(1) 32(−1)2:92 Kr Ar 32:0± 1 33:9(6) 34:0(6) 34:0(6) 31(−3)1:85 Kr Kr 23:0± 1 26:4(15) 23:7(3) 20:6(−10) 22:8(−1)2:85 Kr Kr 25:5± 0:8 26:1(2) 24:7(−3) 24:8(−3) 23:7(−7)1:93 Kr Xe 22:0± 1 22:0(0) 18:9(−14) 18:1(−18) 18:8(−14)2:40 Kr Xe 22:1± 0:7 22:3(1) 19:4(−12) 19:3(−13) 19:5(−12)aIn parenthesis, the percentage deviation of the calculated stopping power values, Scal: from the corresponding experimental values,

Sexp: are quoted i.e. [Scal: − Sexp:]× 100=Sexp:.bBimbot et al. (1989a, b) and Pierce et al. (1968).

Pierce et al. (1968) have been used. The present studieshave been undertaken in order to know the best stoppingpower formulations for gaseous absorbers.

3. Results and discussion

Table 1 presents the experimental stopping power val-ues and the corresponding calculated stopping power valuesalongwith their percentage deviations from the experimen-tal values for projectiles Ne, S, Cl, Ar, Cu and Kr in dif-ferent gas absorbers, e.g. H2, He, N2, Ne, Ar, Kr and Xeat energies ∼ 1–3 MeV=n. It is clear from Table 1 that thestopping power calculations based on SRIM-2000.38 nor-mally provides good overall agreement (within 10%) withthe experimental data for all these projectiles–target combi-nations except H2 gas absorber where SRIM considerablyunderestimates relative to the experimental values. Bentonand Henke and Mukherjee and Nayak formulations providereasonably good agreement with the experimental data ex-cept for Ar, Cu and Kr projectiles in Xe gas target wheresigni�cant deviations are noticed. Northcli�e and Schillingtabulated values considerably underestimate relative to theexperimental stopping power data for Ar and Cu projectilesin Xe and Kr projectile in H2, He and Xe absorbers.Table 2 presents a comparison of calculated stopping

power values with experimental ones for Ne, Ar, Cu, Krand Ag ions in H2, He, N2, Ne, Ar, Kr and Xe absorbers atenergies ∼ 3–13 MeV=n. It is apparent that the calculatedstopping power values from SRIM-2000.38 shows nearly asimilar good trend as already mentioned while discussingTable 1. Again, one notes deviations in H2 gas absorber. The

Benton and Henke formulation provides results which arein good agreement with experimental results except for Cuand Kr projectiles in N2 and Ne absorbers and Ag projec-tile in H2, N2 and Ne gas absorbers. Almost similar behav-ior is noticed in case of Mukherjee and Nayak formulation.Northcli�e and Schilling tabulated values are considerablylower than the experimental data for Ar, Cu, Kr and Agprojectiles in H2 and He gas absorbers. Hubert et al. formu-lation provides good agreement with the experimental datafor Ne, Ar and Cu projectiles in all these gas absorbers ex-cept for Cu projectile in N2 and Ne targets. Further, for Krand Ag projectiles it signi�cantly overestimates the experi-mental values for H2, He and Ar absorbers.Table 3 presents the stopping power data for O (∼ 20–

80 MeV=n), Ar (∼ 20–60 MeV=n), Kr (∼ 20–40MeV=n),Xe, Pb and U (∼ 20–30MeV=n) in H2, He N2, Ne, Ar, Krand Xe gas absorbers. It is noted that SRIM-2000.38 valuesprovide good agreement with experimental data for O, Arand Kr projectiles in all these absorbers. For Xe projectilesigni�cant deviations are noticed for Ar, Kr and Xe gas ab-sorbers. For Pb and U ions this formulation highly overes-timates (as high as up to 40%) the data in all the absorbers.Benton and Henke formulation considerably overestimatesthe experimental data for Xe, Pb and U projectiles in allthese absorbers. Hubert et al. formulation predicts quite asimilar behavior as observed in case of Zielger et al. formu-lation. Mukherjee and Nayak formulation considerably un-derestimates the experimental data for O and Ar projectilesin N2 and Ne gas absorbers. However, the same formulationhighly overestimates (up to 40%) the experimental data forPb and U projectiles in all the gas absorbers.

196 P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202

Table 2Experimental and calculated stopping power values for Ne, Ar, Cu, Kr and Ag projectiles in di�erent gaseous targets in the energy domain∼ 3–13 MeV=na

Energy Projectile Gas Sexpb SRIM2000.38 Benton Mukherjee Northcli�e Hubert(MeV=n) target (MeV=mg cm−2) and and and Schilling et al.

Henke Nayak

5.73 Ne H2 16:2± 0:6 14:4(−11) 15:8(−2) 15:9(−2) 14:8(−9) 15:3(−5)8.28 Ne H2 12:5± 0:9 10:9(−13) 12:1(−3) 12:2(−2) 11:3(−10) 11:5(−8)13.00 Ne H2 8:5± 0:6 7:5(−12) 8:4(−1) 8:4(−1) — 8:0(−6)3.07 Ne He 11:0± 1 10:2(−7) 10:2(−7) — 10:3(−6) 10:1(−8)5.85 Ne He 6:4± 0:4 6:6(3) 6:7(5) — 6:6(3) 6:6(3)8.30 Ne He 5:5± 0:8 5:0(−9) 5:2(−5) — 5:1(−7) 5:1(−7)12.93 Ne He 3:9± 0:2 3:5(−10) 3:7(−5) — — 3:6(−8)5.45 Ne N2 5:9± 0:2 5:8(−2) 5:9(0) 5:8(−2) 5:9(0) 5:9(0)8.18 Ne N2 4:6± 0:1 4:4(−4) 4:5(−2) 4:5(−2) 4:5(−2) 4:5(−2)5.50 Ne Ne 5:3± 0:15 5:1(−4) 5:4(2) 5:4(2) 5:3(0) 5:2(−2)8.15 Ne Ne 4:1± 0:1 4:0(−2) 4:2(2) 4:2(2) 4:1(0) 4:0(−2)12.88 Ne Ne 3:0± 0:1 2:9(−3) 3:0(0) 2:7(−10) — 2:9(−3)5.35 Ne Ar 4:4± 0:1 4:2(−4) 4:3(−2) 4:3(−2) 4:5(2) 4:4(0)8.00 Ne Ar 3:5± 0:1 3:4(−3) 3:4(3) 3:4(−3) 3:5(0) 3:4(−3)12.85 Ne Ar 2:55± 0:08 2:5(−2) 2:5(−2) 2:3(−10) — 2:4(−6)4.70 Ne Kr 3:7± 0:1 3:5(−5) 3:6(−3) 3:8(3) 3:7(0) 3:6(−3)7.70 Ne Kr 2:9± 0:07 2:6(−10) 2:8(−3) 3:1(7) 2:8(−3) 2:8(−3)12.85 Ne Kr 2:05± 0:07 2:0(−2) 2:0(−2) 2:0(−2) — 1:9(−7)5.25 Ne Xe 2:9± 0:08 2:9(0) 2:9(0) 3:1(7) 2:9(0) 2:9(0)7.90 Ne Xe 2:47± 0:06 2:3(−7) 2:3(−7) 2:6(5) 2:4(−3) 2:3(−7)12.8 Ne Xe 1:72± 0:06 1:8(5) 1:7(−1) 1:8(5) — 1:7(−1)3.22 Ar H2 62:0± 3 51:5(−17) 61(−2) 60(−3) 52(−16) 62(0)5.55 Ar H2 47:0± 3 39:6(−16) 46(−2) 45(−4) 38(−19) 45(−4)9.23 Ar H2 32:5± 1:5 28:7(−12) 33(1) 32(−1) 27(−17) 32(−1)3.57 Ar He 25:0± 1 23:0(−8) 24(−4) — 22(−12) 25(0)5.55 Ar He 20:0± 1 18:3(−8) 19(−5) — 17(−15) 19(−5)9.33 Ar He 14:0± 0:8 13:2(−6) 14(0) — 12(−14) 13:9(−1)3.30 Ar N2 18:8± 0:5 19:1(1) 20:5(9) 18:9(0) 18:3(−3) 20:6(9)5.55 Ar N2 14:9± 1:2 15:4(3) 16:2(9) 15:4(3) 14:2(−5) 16:2(9)6.50 Ar N2 13:8± 0:6 14:2(3) 14:9(8) 14:2(3) 13:1(−5) 14:8(7)9.20 Ar N2 11:3± 0:6 11:7(3) 12:1(7) 11:6(3) 10:7(−5) 12:0(6)3.30 Ar Ne 16:7± 0:6 16:7(0) 18:2(9) 16:3(−2) 16:2(−3) 17:7(6)6.30 Ar Ne 12:4± 0:3 12:9(4) 13:7(10) 13:3(7) 12:1(−2) 13:4(8)9.00 Ar Ne 10:7± 0:3 10:8(1) 11:3(6) 10:9(2) 9:9(−7) 10:9(2)3.40 Ar Ar 13:2± 0:5 13:2(0) 13:7(4) 12:9(−2) 13:0(−1) 13:9(5)6.45 Ar Ar 9:9± 0:4 10:5(6) 10:6(7) 10:1(2) 10:0(1) 10:8(9)9.20 Ar Ar 8:3± 0:3 8:9(7) 8:9(7) 8:6(4) 8:3(0) 8:9(7)3.35 Ar Kr 10:1± 0:4 10:2(1) 10:2(1) 9:9(−2) 9:9(−2) 10:3(2)5.30 Ar Kr 8:7± 0:3 8:7(0) 8:9(2) 8:9(2) 8:6(−1) 9:0(3)8.70 Ar Kr 6:9± 0:2 6:9(0) 7:2(4) 7:4(7) 6:7(−3) 7:3(6)3.25 Ar Xe 8:6± 0:3 8:9(3) 8:4(−2) 8:2(−5) 8:4(−2) 8:4(−2)5.35 Ar Xe 7:4± 0:2 7:7(4) 7:3(−1) 7:5(1) 7:2(−3) 7:5(1)8.90 Ar Xe 5:85± 0:15 6:3(8) 6:0(2) 6:3(8) 5:7(−2) 6:1(4)3.17 Cu H2 127:0± 4 101(−20) 124(−1) 124(−2) 97(−24) 132(4)5.95 Cu H2 94:0± 3 78:9(−16) 98:4(5) 95:9(2) 69:4(−26) 96:3(2)6.23 Cu H2 90:0± 3 77:3(−14) 96:2(7) 93:7(4) 67:9(−24) 93:8(4)6.02 Cu He 37:0± 1 36:2(−2) 40:6(10) — 31:4(−15) 40:9(10)6.33 Cu He 38:0± 2 35:3(−7) 39:7(4) — 30:6(−19) 39:9(5)3.10 Cu N2 34:8± 0:9 37:9(9) 40:3(15) 34:2(−2) 34:1(−2) 41:9(20)5.87 Cu N2 29:5± 0:7 30:9(5) 33:6(14) 31:9(8) 26:9(−9) 33:7(14)6.35 Cu N2 28:0± 1 30:0(7) 32:6(16) 30:9(10) 26:1(−7) 32:5(16)3.25 Cu Ne 30:0± 1 32:9(10) 35:1(17) 33:8(13) 29:9(0) 35:4(18)5.75 Cu Ne 25:5± 0:6 27:9(9) 30:3(19) 27:5(8) 24:8(−3) 29:7(16)6.30 Cu Ne 24:8± 0:8 27:1(9) 29:4(18) 26:5(7) 23:9(−4) 28:7(16)

P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202 197

Table 2 (continued)

Energy Projectile Gas Sexpb SRIM2000.38 Benton Mukherjee Northcli�e Hubert(MeV=n) target (MeV=mg cm−2) and and and Schilling et al.

Henke Nayak

3.40 Cu Ar 25:0± 1 25:9(4) 26:1(4) 25:4(2) 24:0(−4) 27:1(8)5.75 Cu Ar 21:9± 0:6 22:7(4) 23:3(6) 22:4(2) 20:6(−6) 23:7(8)6.35 Cu Ar 21:5± 0:8 22:1(3) 22:6(5) 21:6(0) 19:9(−7) 22:9(6)3.25 Cu Kr 18:7± 0:6 20:1(7) 19:2(3) 19:1(2) 18:4(−2) 19:7(5)5.60 Cu Kr 16:9± 0:4 17:5(3) 17:8(5) 17:9(6) 16:3(−3) 18:1(7)6.35 Cu Kr 16:0± 0:6 16:8(5) 17:2(7) 17:3(8) 15:6(−2) 17:5(9)5.40 Cu Xe 14:2± 0:4 15:7(10) 14:7(3) 15:1(6) 13:9(−2) 15:1(6)6.07 Cu Xe 13:9± 0:4 15:3(10) 14:3(3) 14:7(6) 13:4(−3) 14:8(6)3.20 Kr H2 167:0± 11 129(−23) 165(−1) 167(0) 124(−26) 183(9)4.25 Kr H2 155:0± 7 119(−23) 155(0) 155(0) 108(−30) 162(4)5.17 Kr H2 139:0± 8 112(−19) 145(4) 144(3) 99(−29) 147(6)3.10 Kr He 65:0± 3 61:2(−6) 67:0(3) — 56:0(−14) 75:7(16)4.95 Kr He 57:0± 3 52:8(−7) 60:5(6) — 46:0(−19) 63:4(11)5.25 Kr He 54:0± 7 51:6(−4) 59:4(10) — 45:0(−17) 61:7(14)3.20 Kr N2 46:0± 1 48:3(5) 52:3(14) 48:8(6) 43:0(−6) 56:4(23)4.60 Kr N2 41:8± 1:5 44:7(7) 49:3(18) 42:1(1) 39:0(−7) 51:1(22)5.25 Kr N2 40:5± 1:5 43:1(6) 47:6(17) 40:3(0) 37:0(−9) 48:8(20)3.59 Kr Ne 40:5± 1:5 41:6(3) 45:2(12) 44:8(11) 37:8(−7) 46:7(15)4.84 Kr Ne 36:7± 1:5 39:2(7) 43:0(17) 41:0(12) 34:9(−5) 43:4(18)5.10 Kr Ne 35:7± 1:4 38:8(9) 42:5(19) 39:6(11) 34:3(−4) 42:7(20)3.30 Kr Ar 32:0± 1 33:5(5) 33:9(6) 33:9(6) 31:0(−3) 36:4(14)4.25 Kr Ar 30:5± 1:5 32:3(6) 33:1(8) 33:1(8) 30:0(−2) 35:0(15)5.01 Kr Ar 30:0± 1 31:4(5) 32:4(8) 32:0(7) 29:0(−3) 33:8(13)3.40 Kr Kr 24:0± 0:7 25:6(7) 24:7(3) 25:1(3) 23:6(−2) 25:9(8)3.93 Kr Kr 24:2± 0:8 25:1(4) 24:6(2) 25:4(5) 23:2(−4) 25:8(7)4.65 Kr Kr 23:3± 0:9 24:4(5) 24:3(4) 25:1(8) 22:6(−3) 25:4(9)3.25 Kr Xe 21:2± 0:6 22:2(5) 19:8(−7) 20:4(−4) 19:8(−7) 20:8(−2)3.70 Kr Xe 20:0± 0:7 22:0(10) 19:9(0) 20:6(3) 19:6(−2) 20:9(4)4.50 Kr Xe 19:7± 0:7 21:7(10) 19:8(0) 20:7(5) 19:1(−3) 20:8(5)3.80 Ag H2 195± 11 170(−13) 223(14) 232(19) 157(−19) 255(31)3.40 Ag He 93± 4 81(−13) 90(−3) — 73(−21) 108(16)3.87 Ag He 91± 9 79(−13) 89(−2) — 70(−23) 104(14)3.65 Ag N2 61± 2 65(6) 70(15) 71(16) 58(−5) 79(29)3.85 Ag N2 58± 3 64(10) 70(21) 71(22) 57(−2) 78(34)3.70 Ag Ne 55± 2 57(4) 61(11) 63(14) 51(−7) 66(20)3.33 Ag Ar 44:2± 1:5 45:6(3) 45:2(2) 48(8) 42(−5) 51:2(16)3.78 Ag Ar 44:0± 2 45:3(3) 45:3(3) 48(9) 42(−4) 50:6(15)3.50 Ag Kr 34± 1 35(3) 33(−3) 35(3) 32(−6) 36(6)3.85 Ag Kr 33± 2 35(6) 33(0) 36(9) 32(−3) 36(9)3.40 Ag Xe 29± 1 30(3) 26(−10) 28(−3) 27(−7) 29(0)aIn parenthesis, the percentage deviation of the calculated stopping power values, Scal: from the corresponding experimental values,

Sexp: are quoted i.e. [Scal: − Sexp:]× 100=Sexp:.bBimbot et al. (1989a, b).

Table 4 presents the experimental as well as calculatedstopping power values for Ne, Ar, Cu and Kr ions in CH4,C4H10, CO2 and CF4 complex gas absorbers in the ionenergy range ∼ 1–3 MeV=n. It is noted that the calcu-lated stopping power values based on SRIM-2000.38 arein quite a close agreement with experimental data for allthese projectile–target combinations. Benton and Henke for-mulation shows signi�cant deviation for Ar, Cu and Krprojectiles in CH4 and C4H10 absorbers. Mukherjee andNayak formulation provides a general good agreement but

signi�cant deviations are noted for Ar projectile in CF4absorber.In Table 5, the comparison between the calculated and

experimental stopping power values for Ne, Ar, Cu, Krand Ag projectiles in CH4, C4H10, CO2 and CF4 ab-sorbers is depicted in energy range (∼ 3–13 MeV=n).SRIM-2000.38 values are again in close agreement withexperimental data for all these projectile–target combi-nations. Benton and Henke formulation highly overesti-mates (up to ∼ 30%) the experimental data except for Ne

198 P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202

Table 3Experimental and calculated stopping power values for O(∼ 20–80 MeV=n), Ar(∼ 20–60 MeV=n), Kr(∼ 20–40 MeV=n), Xe, Pb andU(∼ 20–30 MeV=n) projectiles in di�erent gaseous targetsa

Energy Projectiles Gas Sexpb SRIM2000.38 Benton and Mukherjee Hubert(MeV=n) target (MeV=mg cm−2) Henke and Nayak et al.

23.94 O H2 3:25± 0:13 3:04(−6) 3:57(9) 3:18(−2) 3:11(−4)23.94 O He 1:48± 0:07 1:39(−6) 1:39(−6) — 1:41(−5)20.96 O N2 1:41± 0:02 1:42(1) 1:39(−1) 1:10(−22) 1:40(−1)83.34 O N2 0:48± 0:02 0:47(−2) 0:46(−4) 0:33(−31) 0:47(−2)23.74 O Ne 1:19± 0:04 1:18(−1) 1:18(−1) 1:02(−14) 1:16(−2)83.63 O Ne 0:45± 0:03 0:44(−2) 0:44(−2) 0:35(−22) 0:44(−2)23.01 O Ar 1:04± 0:02 1:05(1) 1:00(−4) 0:93(−10) 1:01(−3)83.26 O Ar 0:36± 0:016 0:38(5) 0:37(3) 0:32(−11) 0:38(5)22.12 O Kr 0:88± 0:01 0:90(2) 0:86(−2) 0:85(−3) 0:87(−1)82.36 O Kr 0:33± 0:009 0:33(0) 0:32(−3) 0:29(−12) 0:33(0)80.82 O Xe 0:30± 0:006 0:30(0) 0:29(−3) 0:27(−10) 0:30(0)29.42 Ar H2 13:2± 0:5 12:7(−4) 13:3(1) 13:3(1) 12:9(−2)43.19 Ar H2 9:5± 0:9 9:5(0) 9:7(2) 9:5(0) 9:5(0)56.25 Ar H2 7:9± 0:6 7:7(−2) 7:8(−1) 7:6(−4) 7:7(−2)29.48 Ar He 5:9± 0:25 5:8(−2) 5:9(0) — 5:9(0)43.58 Ar He 4:0± 1:5 4:3(7) 4:3(7) — 4:3(7)56.76 Ar He 3:5± 0:5 3:5(0) 3:5(0) — 3:5(0)40.14 Ar N2 4:10± 0:04 4:19(2) 4:15(1) 3:18(−22) 4:16(1)55.51 Ar N2 3:25± 0:12 3:26(0) 3:22(−1) 2:40(−26) 3:25(0)40.76 Ar Ne 3:71± 0:04 3:84(3) 3:88(4) 3:27(−12) 3:79(2)55.91 Ar Ne 3:00± 0:15 3:01(0) 3:03(1) 2:48(−17) 2:99(0)42.07 Ar Ar 3:17± 0:07 3:25(2) 3:15(−1) 2:85(−10) 3:17(0)27.84 Ar Kr 3:50± 0:04 3:72(6) 3:58(2) 3:56(2) 3:59(2)40.89 Ar Kr 2:69± 0:03 2:81(4) 2:72(1) 2:61(−3) 2:74(2)52.55 Ar Kr 2:26± 0:03 2:33(3) 2:26(0) 2:12(−6) 2:29(1)26.79 Ar Xe 3:19± 0:03 3:43(7) 3:21(1) 3:25(2) 3:25(2)40.17 Ar Xe 2:44± 0:02 2:57(5) 2:44(0) 2:39(−2) 2:47(1)55.65 Ar Xe 2:00± 0:07 2:02(1) 1:93(−3) 1:84(−8) 1:97(−1)21.42 Kr H2 58:6± 1:3 55:6(−5) 63:9(9) 61:6(5) 61:0(4)22.84 Kr H2 54:7± 3:3 53:7(−2) 61:0(11) 58:7(5) 58:3(6)22.40 Kr He 25:1± 1:1 24:9(−1) 26:9(7) — 26:4(5)42.40 Kr He 17:0± 3 16(−6) 17(0) — 17(0)24.12 Kr N2 21:6± 0:9 21:7(0) 22:4(4) 20:9(−3) 21:9(1)41.82 Kr N2 14:7± 0:7 15:2(3) 15:3(4) 14:1(−4) 15:2(3)23.12 Kr Ne 19:5± 0:4 20:6(6) 21:5(10) 20:2(3) 20:5(5)41.70 Kr Ne 13:6± 0:6 14:1(4) 14:4(6) 13:4(−1) 13:9(2)22.46 Kr Ar 16:7± 0:3 18:1(8) 17:7(6) 16:6(0) 17:5(5)41.70 Kr Ar 11:5± 0:5 12:3(7) 11:9(3) 10:9(−5) 11:9(3)40.83 Kr Kr 9:75± 0:15 10:7(10) 10:2(5) 9:6(−1) 10:2(5)41.68 Kr Kr 9:7± 0:3 10:4(7) 9:9(2) 9:3(−4) 9:9(2)41.64 Kr Xe 8:55± 0:25 9:4(10) 8:7(2) 8:3(−3) 8:8(3)25.54 Xe H2 106± 5 99(−7) 119(12) 113(7) 111(5)26.55 Xe He 44± 6 44(0) 50(14) — 48(9)25.64 Xe N2 39:6± 1 41:3(4) 44:6(13) 41:2(4) 42:5(7)25.65 Xe Ne 35:3± 0:8 38:2(8) 41:3(17) 38:5(9) 38:4(9)26.03 Xe Ne 35:0± 1:2 37:9(8) 40:9(17) 38:1(9) 38:1(9)25.75 Xe Ar 28:1± 0:8 32:9(17) 33:1(18) 30:8(10) 31:9(13)24.74 Xe Kr 21:8± 0:3 28:1(29) 27:2(25) 25:9(5) 26:6(22)25.72 Xe Kr 22:2± 0:6 27:6(24) 26:7(20) 25:4(−1) 26:1(17)24.63 Xe Xe 18:4± 0:3 25:1(36) 23:0(25) 23:0(−7) 23:1(25)26.67 Pb Ne 60:6± 1:8 71(7) 81(34) 77(27) 72(19)27.65 Pb Ne 62± 3 70(13) 80(29) 75(21) 71(14)26.38 Pb Ar 50± 1:5 62(24) 65(30) 60(20) 60(20)27.69 Pb Ar 47:4± 2:4 61(29) 63(33) 58(22) 59(24)26.06 Pb Kr 41± 1 52(27) 51(24) 50(22) 48(17)

P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202 199

Table 3 (continued)

Energy Projectiles Gas Sexpb SRIM2000.38 Benton and Mukherjee Hubert(MeV=n) target (MeV=mg cm−2) Henke and Nayak et al.

27.57 Pb Kr 39± 2 51(31) 50(28) 49(26) 47(20)27.09 Pb Xe 34:6± 1 46(33) 43(24) 44(27) 41(18)27.91 Pb Xe 32:4± 2 45(39) 42(30) 43(33) 41(26)21.87 U N2 86± 3:5 98(14) 116(35) 111(29) 105(22)22.91 U N2 86± 6 96(12) 114(32) 108(25) 102(19)22.03 U Ar 60± 2 78(30) 82(37) 79(32) 76(27)22.94 U Ar 60± 3:3 77(28) 81(35) 77(28) 74(23)21.89 U Kr 47:3± 1:4 65(37) 64(35) 66(39) 60(27)22.94 U Kr 46± 2 64(40) 63(37) 65(41) 59(28)21.86 U Xe 42:2± 1:3 58(37) 53(25) 57(35) 51(21)22.94 U Xe 39± 2 57(46) 53(36) 56(43) 51(31)aIn parenthesis, the percentage deviation of the calculated stopping power values, Scal: from the corresponding experimental values,

Sexp: are quoted i.e. [Scal: − Sexp:]× 100=Sexp:.bBimbot et al. (1996) and Herault et al. (1991).

Table 4Experimental and calculated stopping power values for Ne, Ar, Cu and Kr projectiles in complex gaseous targets at energies ∼ 1–3 MeV=na

Energy Projectile Gas target Sexpb SRIM-2000.38 Benton and Mukherjee(MeV=n) (MeV=mg cm−2) Henke and Nayak

2.26 Ne CH4 13:6± 0:4 13.7(1) 14.9(9) 13.9(2)2.88 Ne CH4 12:3± 0:5 12.1(−2) 13.1(6) 12.5(2)2.33 Ne C4H10 12:3± 0:4 12.3(0) 13.2(7) 12.3(0)2.88 Ne C4H10 11:0± 0:3 10.9(−1) 11.9(8) 11.2(2)2.32 Ne CO2 9:0± 0:3 9.1(1) 9.5(5) 8.7(−3)2.77 Ne CO2 8:3± 0:3 8.4(1) 8.8(6) 8.1(−2)2.90 Ne CO2 8:1± 0:2 8.2(1) 8.6(6) 7.9(−2)2.52 Ne CF4 8:2± 0:2 8.3(1) 8.3(1) 7.7(−6)2.87 Ne CF4 7:6± 0:3 7.8(3) 7.8(3) 7.3(−4)1.80 Ar CH4 34:0± 1 33.4(−2) 38.2(12) 33.1(−3)2.11 Ar CH4 31:7± 1:5 32.2(2) 36.8(16) 32.3(2)1.97 Ar C4H10 30:0± 1 29.8(0) 33.5(12) 28.5(−5)2.70 Ar C4H10 27:0± 0:9 27.2(1) 30.7(14) 27.9(3)3.00 Ar C4H10 26:3± 0:9 26.1(−1) 29.5(12) 26.1(−1)2.12 Ar CO2 21:3± 0:8 21.7(2) 23.2(9) 19.1(−10)1.53 Ar CF4 22:8± 0:7 21.5(−6) 21.8(−4) 18.7(−18)1.91 Ar CF4 21:2± 0:8 20.8(−2) 21.2(0) 18.6(−12)1.90 Cu CH4 58:0± 3 61.4(6) 67.8(17) 64.0(10)2.00 Cu C4H10 52:0± 2 55.4(6) 60.3(16) 57.0(10)2.12 Cu C4H10 51:0± 3 54.9(8) 60.1(18) 56.1(10)1.78 Cu CO2 40:2± 1:5 41.4(3) 41.9(4) 37.1(−8)2.12 Cu CO2 38:0± 3 40.7(7) 41.8(10) 37.8(0)1.93 Cu CF4 37:0± 2 38.7(4) 37.3(1) 34.2(−7)2.93 Cu CF4 33:6± 0:9 36.2(8) 36.4(8) 33.7(0)2.15 Kr CH4 73:0± 4 75(3) 85(16) 83(14)2.95 Kr CH4 69:0± 2 71(3) 84(22) 78(13)1.94 Kr C4H10 68:0± 3 68(0) 76(12) 73(7)2.57 Kr C4H10 66:0± 2 66(0) 76(15) 74(12)1.98 Kr CO2 49:0± 2 50(2) 52(6) 48(−2)2.40 Kr CO2 49:5± 1:5 50(1) 53(7) 50(1)1.93 Kr CF4 46:0± 2 47(2) 47(2) 43(−6)2.78 Kr CF4 45:0± 2 46(2) 47(4) 45(0)aIn parenthesis, the percentage deviation of the calculated stopping power values, Scal: from the experimental values, Sexp: are quoted i.e.

[Scal: − Sexp:]× 100=Sexp:.bBimbot et al. (1989a, b).

200 P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202

Table 5Experimental and calculated stopping power values for Ne, Ar, Cu, Kr and Ag projectiles in complex gaseous targets in energy domain∼ 3–13 MeV=na

Energy Projectiles Gas Sexpb SRIM−2000.38 Benton and Mukherjee Hubert(MeV=n) target (MeV=mg cm−2) Henke and Nayak et al.

5.00 Ne CH4 9:1± 0:3 8.7(−4) 9.3(2) 9.1(0) 8.9(−2)8.30 Ne CH4 6:6± 0:3 6.1(−7) 6.5(−1) 6.5(−1) 6.2(−6)13.00 Ne CH4 4:4± 0:3 4.3(−2) 4.5(2) 3.9(−11) 4.4(0)5.08 Ne C4H10 8:2± 0:2 7.9(−4) 8.4(2) 8.2(0) 7.9(−4)7.30 Ne C4H10 6:5± 0:15 6.2(−5) 6.5(0) 6.4(−1) 6.2(−5)12.7 Ne C4H10 4:05± 0:15 4.1(1) 4.2(4) 3.6(−11) 4.1(1)4.70 Ne CO2 6:45± 0:15 6.3(−2) 6.5(1) 6.3(−2) 6.3(−2)7.80 Ne CO2 4:7± 0:1 4.5(−4) 4.7(0) 4.6(−2) 4.5(−4)5.25 Ne CF4 5:65± 0:15 5.7(1) 5.5(−3) 5.4(−4) 5.4(−4)8.10 Ne CF4 4:45± 0:15 4.3(−3) 4.2(−6) 4.2(−6) 4.1(−8)5.20 Ar CH4 22:0± 1 22.6(3) 25.3(15) 24.1(9) 24.3(10)9.30 Ar CH4 15:7± 0:8 16.2(3) 17.5(11) 17.0(8) 16.8(7)4.10 Ar C4H10 22:6± 0:5 23.1(2) 25.9(15) 24.4(8) 24.9(10)5.60 Ar C4H10 19:7± 0:5 19.9(1) 21.9(11) 20.9(6) 21.0(6)5.10 Ar CO2 15:4± 0:5 15.9(3) 16.9(10) 15.8(2) 16.4(6)8.70 Ar CO2 11:6± 0:3 12.1(4) 12.6(9) 11.9(2) 12.2(5)9.10 Ar CO2 11:4± 0:4 11.7(3) 12.2(7) 11.6(2) 11.8(3)3.30 Ar CF4 17:3± 0:6 18.0(4) 18.5(7) 16.2(−6) 18.1(5)6.25 Ar CF4 13:1± 0:3 13.9(6) 13.8(5) 13.2(1) 13.5(3)9.20 Ar CF4 10:7± 0:3 11.4(6) 11.1(4) 10.7(0) 10.8(1)3.20 Cu CH4 50:0± 1:5 54.7(9) 63.3(27) 56.4(13) 65.0(30)5.90 Cu CH4 42:0± 1 43.9(4) 51.2(22) 48.9(16) 49.7(18)6.30 Cu CH4 39:6± 1:5 42.7(8) 49.6(25) 47.5(20) 48.1(21)5.05 Cu C4H10 40:9± 0:9 42.7(4) 49.3(20) 46.9(15) 48.6(19)6.20 Cu C4H10 36:0± 1 39.4(9) 45.1(25) 43.1(20) 43.8(22)3.10 Cu CO2 34:6± 0:9 37.7(9) 40.3(16) 35.6(3) 40.6(17)5.92 Cu CO2 28:4± 0:7 30.7(8) 33.5(18) 31.4(10) 32.7(15)3.30 Cu CF4 32:0± 1 35.3(10) 35.8(12) 32.2(1) 36.1(13)5.90 Cu CF4 27:1± 0:7 29.7(9) 30.4(12) 28.4(5) 29.8(10)3.55 Kr CH4 65:0± 3 68(5) 82(26) 74(14) 86(32)4.78 Kr CH4 62:0± 2 63(2) 76(22) 71(14) 77(24)5.15 Kr CH4 60:0± 3 62(3) 74(23) 72(20) 74(23)5.05 Kr C4H10 56:0± 2 57(2) 67(20) 65(16) 67(20)3.15 Kr CO2 46:5± 1:5 48(3) 52(12) 48(3) 54(16)4.87 Kr CO2 41:5± 1:5 44(6) 49(18) 42(1) 49(18)4.30 Kr CF4 40:5± 1:5 43(6) 45(11) 41(1) 46(13)4.90 Kr CF4 38:0± 1:5 42(10) 44(16) 40(5) 44(16)3.65 Ag CH4 90:0± 3 93(3) 112(24) 112(24) 125(39)3.82 Ag CH4 86:0± 6 93(8) 112(30) 109(27) 123(43)3.03 Ag C4H10 88:0± 3 87(−1) 101(15) 103(17) 115(31)3.87 Ag C4H10 78:0± 6 84(8) 100(28) 95(22) 109(40)aIn parenthesis, the percentage deviation of the calculated stopping power values, Scal: from the experimental values, Sexp: are quoted i.e.

[Scal: − Sexp:]× 100=Sexp:.bBimbot et al. (1989a, b).

projectile. Mukherjee and Nayak formulation shows sig-ni�cant deviations for Cu, Kr and Ag projectiles in CH4and C4H10 absorbers. Hubert et al. formulation shows rea-sonably good agreement with the experimental data for Neand Ar projectile but it highly overestimates the experi-mental values for Cu, Kr and Ag projectiles, in all theseabsorbers.

In Table 6, the stopping power data for O (∼ 20–80 MeV=n), Ar (∼ 40–55 MeV=n), Kr (∼ 20–40 MeV=n),Xe, Pb and U (∼ 20–30 MeV=n) in CH4, C4H10, CO2 andCF4 gas absorbers is presented. It is noted that the cal-culations based on SRIM-2000.38 are in good agreementwith the experimental data for O, Ar and Kr projectiles.However, signi�cant deviations are noted for Xe, Pb and

P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202 201

Table 6Experimental and calculated stopping power values for O(∼ 20–80 MeV=n), Ar(∼ 20–60 MeV=n), Kr(∼ 20–40 MeV=n), Xe, Pb andU(∼ 20–30 MeV=n) projectiles in complex gaseous targetsa

Energy Projectiles Gas Sexpb SRIM-2000.38 Benton and Mukherjee Hubert et al.(MeV=n) target (MeV=mg cm−2) Henke and Nayak

22.18 O CH4 1:88± 0:03 1.85(−1) 1.86(−1) 1.61(−14) 1.84(−2)83.52 O CH4 0:66± 0:04 0.64(−3) 0.64(−3) 0.50(−24) 0.64(−3)22.59 O C4H10 1:72± 0:03 1.68(−2) 1.68(−2) 1.41(−18) 1.67(−3)24.06 O C4H10 1:66± 0:06 1.59(−4) 1.59(−4) 1.33(−20) 1.58(−5)22.33 O CO2 1:34± 0:02 1.34(0) 1.32(−1) 1.05(−22) 1.32(−1)24.06 O CO2 1:29± 0:04 1.26(−2) 1.24(−4) 0.99(−23) 1.24(−4)82.92 O CO2 0:47± 0:016 0.47(0) 0.47(0) 0.34(−28) 0.47(0)22.45 O CF4 1:24± 0:02 1.26(2) 1.22(−2) 1.01(−18) 1.21(−2)24.04 O CF4 1:19± 0:05 1.19(0) 1.15(−3) 0.96(−19) 1.15(−3)81.52 O CF4 0:45± 0:009 0.44(−2) 0.44(−2) 0.33(−27) 0.44(−2)40.20 Ar CH4 5:58± 0:05 5.7(2) 5.7(2) 4.8(−14) 5.6(0)55.92 Ar CH4 4:50± 0:2 4.4(−2) 4.4(−2) 3.6(−20) 4.4(−2)40.49 Ar C4H10 5:24± 0:05 5.21(0) 5.25(0) 4.27(−18) 5.16(−1)52.69 Ar C4H10 4:33± 0:06 4.25(−2) 4.25(−2) 3.39(−22) 4.22(−2)41.47 Ar CO2 3:99± 0:05 4.05(1) 4.05(1) 3.11(−22) 4.01(0)52.42 Ar CO2 3:36± 0:05 3.37(0) 3.36(0) 2.54(−24) 3.36(0)40.03 Ar CF4 3:77± 0:03 3.88(3) 3.87(3) 3.12(−17) 3.82(1)54.29 Ar CF4 3:04± 0:06 3.06(1) 3.04(0) 2.39(−21) 3.03(0)22.67 Kr CH4 30:9± 0:5 30.8(0) 33.3(8) 31.6(2) 31.7(2)41.72 Kr CH4 21:0± 1 20.7(−1) 21.4(2) 20.0(−5) 20.7(−1)22.69 Kr C4H10 28:0± 2 28.4(1) 30.4(8) 28.8(2) 28.9(2)24.14 Kr C4H10 26:8± 1:3 27.3(2) 29.1(8) 27.6(3) 27.8(4)41.84 Kr C4H10 18:8± 0:7 19.1(1) 19.5(4) 18.3(−3) 18.9(0)22.60 Kr CO2 21:9± 0:4 22.5(3) 23.4(7) 21.7(−1) 22.5(3)41.66 Kr CO2 15:0± 0:4 15.1(1) 15.3(2) 14.0(−7) 14.9(−1)22.56 Kr CF4 19:7± 0:3 21.3(8) 21.6(10) 20.2(2) 20.8(5)41.71 Kr CF4 13:7± 0:4 14.1(3) 13.9(1) 13.1(−4) 13.8(1)25.33 Xe CH4 57:1± 1:1 56.7(−1) 64.5(13) 60.4(6) 60.3(6)24.79 Xe C4H10 51:2± 0:9 52.8(3) 59.7(17) 55.7(9) 55.7(9)25.81 Xe CO2 38:5± 1:2 40.8(6) 44.4(15) 40.6(5) 41.6(8)24.79 Xe CF4 33:9± 0:6 39.4(16) 41.8(23) 38.7(14) 39.2(16)25.75 Xe CF4 33:9± 1:1 38.6(14) 40.9(21) 37.8(11) 38.4(13)26.35 Pb CH4 102± 3 105(3) 130(27) 122(20) 118(16)27.65 Pb CH4 99:0± 5 103(4) 127(28) 118(19) 115(16)26.22 Pb C4H10 92:0± 3 97(5) 118(28) 111(21) 107(16)27.63 Pb C4H10 87:0± 4 95(9) 115(32) 107(23) 104(19)22.65 Pb CO2 69:0± 2 77(11) 89(29) 82(19) 80(16)27.69 Pb CF4 58:0± 3 71(22) 80(38) 74(27) 72(24)22.00 U CF4 68:6± 2:7 92(34) 105(53) 101(47) 94(37)22.96 U CF4 69:0± 4 90(30) 103(49) 99(43) 92(33)aIn parenthesis, the percentage deviation of the calculated stopping power values, Scal: from the experimental values, Sexp: are quoted i.e.

[Scal: − Sexp:]× 100=Sexp:.bBimbot et al. (1996) and Herault et al. (1991).

U projectiles in CF4 absorber. Benton and Henke formu-lation shows reasonably good agreement with the data forO, Ar and Kr projectiles. For Xe, Pb and U projectiles,it highly overestimates the experimental values. Mukher-jee and Nayak formulation considerably underestimatesthe experimental values for O and Ar projectiles, showsreasonably good agreement for Kr and Xe projectiles andsigni�cantly overestimates for Pb and U projectiles. Hubertet al. formulation provide reasonably good agreement with

experimental data for O, Ar and Kr projectiles but signi�-cantly overestimates the data for Xe, Pb and U projectiles.

4. Conclusions

1. The calculated stopping power values based on Ziegler etal. formulation using SRIM-2000.38 shows good overallagreement with experimental data for projectiles Z = 8–

202 P.K. Diwan et al. / Radiation Measurements 33 (2001) 193–202

47 in all gas absorbers except H2, where the formulationsigni�cantly underestimates the experimental data. Forhigher Z projectiles (Z =54–92), the formulation highlyoverestimates the experimental values in nearly all theabsorbers.

2. Barring a few exceptions, Benton and Henke formulationshows reasonably good agreement for Z = 8–47 projec-tiles in elemental absorbers. In case of complex absorbers,no systematic trend is visible, indicating large deviationsin many cases.

3. Mukherjee and Nayak formulation shows generally rea-sonable agreement for Z = 8–54 projectiles in elementalgas absorbers. Signi�cant deviations are noticed in caseof Pb and U projectiles. No systematic trend is discern-able for complex media.

4. Northcli�e and Schilling tabulated values normally showsigni�cant deviations for H2, He and Xe absorbers.

5. Hubert et al. formulation highly overestimates the experi-mental stopping power values for projectiles Z=29–54 innearly all the gas absorbers. However, for all these projec-tiles, this formulation shows excellent agreement in caseof solid absorbers (Sharma et al., 1995a). Such discrimi-nation may be attributed to the change in the phase stateof the absorber (gas–solid e�ect). A lesser ionic chargefor projectiles in gaseous media may result in a smallerstopping power compared to solid absorbers.Finally, it is concluded that for projectile ions Z6 47 the

calculated stopping power values based on SRIM-2000.38are in good agreement with the experimental data in all thegaseous absorbers considered in the present study exceptfor H2. In case of H2 gas absorbers, Benton and Henke for-mulation provides better agreement. For heavier projectileslike Xe, Pb and U, all formulations considered in the presentstudy highly overestimates the experimental results.

Acknowledgements

We are extremely grateful to Prof. N. Nath and Dr. San-jeev Aggarwal, Kurukshetra University, Kurukshetra formany important suggestions and kind co-operation duringthis work. One of the authors (P.K. Diwan) is grateful tothe Department of Science and Technology, New Delhi,India for providing �nancial assistance.

References

Ahlen, S.P., 1980. The theoretical and experimental aspects of theenergy loss of relativistic heavily ionizing particles. Rev. Mod.Phys. 52, 121–173.

Benton, E.V., Henke, R.P., 1969. Heavy particle range energyrelations for dielectric nuclear track detectors. Nucl. Instr. andMeth. 67, 87–92.

Bimbot, R., Barbey, S., Benfoughal, Clapier, F., Mirea, Pauwels,N., Pierre, S., Rivet, M.F., Fares, G., Hachem, A., Anne, R.,Georget, Y., Hue, R., Tribouillard, C., 1996. Stopping power ofgases for heavy ions. Nucl. Instr. and Meth. B107, 9–14.

Bimbot, R., Cabot, C., Gardes, D., Gauvin, H., Hingmann, R.,Orliange, I., Reilhac, L.De, Hubert, F., 1989a. Stopping powerof gases for heavy ions: gas–solid e�ect. Nucl. Instr. and Meth.B44, 1–18.

Bimbot, R., Cabot, C., Gardes, D., Gauvin, H., Hingmann, R.,Orliange, I., Reilhac, L.De, Subotic, K., Hubert, F., 1989b.Stopping power of gases for heavy ions: gas–solid e�ect. Nucl.Instr. and Meth. B44, 19–34.

Geissel, H., Laichter, Y., Schneider, W.F.W., Armbruster, P., 1982.Observation of a gas–solid di�erence in the stopping powers of(1–10) MeV/u heavy ions. Phys. Lett. 88A (1), 26–28.

Geissel, H., Laichter, Y., Schneider, W.F.W., Armbruster, P., 1983.On the e�ective charges from stopping powers of 0.5–10 MeV/uheavy ions. Phys. Lett. 99A (2,3), 77– 80.

Herault, J., Bimbot, R., Gauvin, H., Kubica, B., Anne, R., Bastin,G., Hubert, F., 1991. Stopping power of gases for heavy ions (O,Ar, Kr, Xe) at intermediate energy (20–100 MeV=u). Vanishingof the gas–solid e�ect. Nucl. Instr. and Meth. B61, 167–174.

Hubert, F., Bimbot, R., Gauvin, H., 1989. Semi-empirical formulaefor heavy ion stopping in solids in the intermediate energy range.Nucl. Instr. and Meth. B36, 357–363.

Kapoor, S.S., Ramamurthy, V.S., 1986. Nuclear RadiationDetectors. Wiley Eastern Limited, New Delhi, India.

Kumar, S., Sharma, S.K., Nath, N., Harikumar, V., Pathak, A.P.,Hui, S.K., Kabiraj, D., Avasthi, D.K., 1997. Energy loss of MeVheavy ions in carbon. Vacuum 48, 1027–1029.

Mukherjee, S., Nayak, A.K., 1979. Calculation of heavy ion rangein complex media. Nucl. Instr. and Meth. 159, 421–431.

Northcli�e, L.C., Schilling, R.F., 1970. Range and stopping powertables for heavy ions. At. Data Nucl. Data Tables A7, 233–463.

Pierce, T.E., Blann, M., 1968. Stopping powers and ranges of5–90 MeV S32 Cl35, Br79 and I127 ions in H2, He, N2, Ar andKr: a semiempirical stopping power theory for heavy ions ingases and solids. Phys. Rev. 173 (2), 390–405.

Randhawa, G.S., Virk, H.S., 1996. Stopping power and range ofheavy ions in solids: a comparative study. Radiat. Meas. 26,541–560.

Sharma, S.K., Kumar, S., Sharma, A.P., 1995a. Range ofheavy ions in solids: a compartive study. Appl. Radiat. Isot. 46,1345–1350.

Sharma, S.K., Kumar, S., Yadav, J.S., Sharma, A.P., 1995b.Stopping power of heavy ions in solids: a comparative study.Appl. Radiat. Isot. 46, 39–52.

Ziegler, J.F., 1999. Stopping of energetic light ions in elementalmatter. J. Appl. Phys. 85 (3), 1249–1272.

Ziegler, J.F., Biersack, J.P., Littmark, U., 1985. The Stopping andRange of Ions in Solids, Vol. 1. Pergamon Press, New York.