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Gamma-ray strength statistics applied to the 25Mg(p, γ)26Al reaction
Volume 173, number 3
PHYSICS LETTERS B
12 June 1986
G A M M A - R A Y S T R E N G T H S T A T I S T I C S APPLIED TO THE 2SMg(p, ~)Z6A! REACTION P.M. E N D T , C. A L D E R L I E S T E N
and P. D E W I T
Fysisch Laboratorium, Rijksuniversiteit Utrecht, P.O. Box 80000, 3508 TA Utrecht, The Netherlands
Received 27 February 1986
For 1250 out of 2700 y-ray transitions observed in 26A1by means of the 25Mg(p, ~)26A1 reaction the transition character (M1Ev,Mlm, Elw, Elm, E2 m or E2w, with IV and IS standing for isovector and isoscalar, respectively) and the strength (in W.u.) have been determined. The (logarithmic) average strengths for these six groups of transitions turn out to have a wide applicabilityin nuclear spectroscopy. They have been used for the determination of parities and isospins of (p, ~) resonances and bound states, and they provide a measure of Fp0/F (Fp0 ground-state proton width, F total width) for those resonances which had not been observed in previous 25Mg(p, Po) work.
The strength averages for 3,-ray transitions of the same character (split up according to multipolarity, E or M, A T = 0 or A T = 1) have almost been disregarded in nuclear spectroscopy. The use of such averages was even strongly discouraged [1] because it was argued that future more refined detection methods (more sensitive detecors, lower background etc.) would result in the detection o f many more weak transitions, thus lowering the averages. The present paper will show that y e t gamma-ray strength statistics (GRSS) can be extremely useful, provided that they are based on a large and homogeneous set o f transitions, all observed in the same nucleus with the same reaction and the same detection set-up. The set o f transitions considered here stems from the 25Mg(p, 7)26A1 reaction investigated at 75 resonances in the Ep = 0 . 3 1 - 1 . 8 4 MeV region. Spectra with good statistics (up to 3000/2Ah) have been taken with 8 0 - 1 1 0 cm 3 Ge and Ge(Li) detectors at angles of 55 ° and 90 ° to the proton beam (the 55 ° detector provided with a Compton suppression shield), for the measurement o f 3'-ray intensities and energies, respectively. Altogether 84 lower states are excited in the resonance decay. In addition about 40 resonance -+ resonance transitions were found. Many resonances and lower states had not been observed previously. Accurate energies (AE x = 3 0 - 2 0 0 eV) have been measured except for some broad resonances, and lifetimes (or lifetime limits) have been obtained for
most bound states from measured Doppler shifts. The number o f observed transitions between bound states amounts to 530 and that o f primary transitions from the resonances to 2130. For many states the abovementioned detailed spectral information combined with data from other reactions provides unambiguous assignments of spin, parity and isospin ( T - 0 or 1). In addition to the information given in the most recent A = 2 1 - 4 4 compilation [2], data from the 28Si(~, c026A1 [3] and 25Mg(p, p0)25Mg [4] reactions have been particularly useful, the former providing parities (natural or unnatural) of many bound states, whereas from the latter /-values (and thus parities) have been obtained for 39 resonances in the Ep = 0 . 8 0 - 1 . 8 4 MeV region. We now have resonances with 22 different J r r ; T assignments (J = 1 - 5 with 7r = +, T = 0 and T = 1, two 6 - ;0 resonances and a probable 0 - ; 0 resonance). The "),-ray based j~r ; T assignments (or limitations) make use of recommended upper limits (RUL's) for 3,-ray strengths, defined in ref. [ 1 ]. F r o m the present very large set o f transitions in 26A1 (many more than the 950 transitions between bound states in the whole A = 6 - 4 4 region discussed in ref. [1 ]) upper limits have been derived for some important transition characters (for use in 26A1 only). They are 0.002, 0.05, 5 and 50 W.u. for Ells, M i l s , E21V and E2IS , respectively, to be compared to 0.003, 0.03, 10 and 100 W.u. in ref. [1]. The differences are seen to be at most 225
Volume 173, number 3
PHYSICS LETTERS B
Oh
o~ I~
g,
ee~
¢.q
g
m~ i
I
< ~a O II
g
g ~q
e~4
t--- I
g eq
~D
oO
eq
mel
g.
I
,-;,
g
Paa,
~,-g
eq <-,i
-g O
_o g ea
+g O
t •
226
O
12 J u n e 1 9 8 6
a factor of 2. No M2 transitions (only five are observed) or transitions of higher multipolarity are considered in the present paper; almost any such transition exceeding the detection limit would exceed the corresponding RUL's set in ref. [1]. Strength averages for 1249 transitions proceeding between states with known j,r ; T are given in table 1. None of these transitions exceed the upper limits mentioned above. All transitions are considered to be unmixed (8 = 0). From previous work [2] the mixing ratios are known of only nine transitions between bound states, and the present work has not offered any new information (angular distribution measurements have not been performed). Resonances were only taken for which P p o / P had been measured, mostly from (p, P0) [4], and which could be considered as virtually isospin-pure. The most sensitive measure of T-purity is the strength average for M I I s and/or E1 IS. A significant excess of these averages over the bound-state averages points to T-mixing A very clear case of T-mixing is offered by the pair resonances at Ep = 1205 and 1237 keV, both with j,r = 3 +. The 45-branch decay is almost identical, and the M I l v and M I I s averages are equal to within the combined error. Another 8 resonances were also rejected because of considerable T-mixing with strong resonances with the same jTr in the neighbourhood. The strength distributions for different transition character have rather different widths. The RMS logarithmic deviation from the average for a single transition amounts to A log S = 0.79, 0.50, 0.56, 0.63, 0.86 and 0.88 for M I l v , MIls, E I I v , Ells, E2ts and E2IV, respectively. A comparison of the bound -+ bound and resonance -+ bound averages in table 1 shows that for all transition characters the averages are equal within twice the combined error except for M I I s . Apparently some of the resonances taken still contain weak T-admixtures. The differences are not considered large enough, however, to prevent us from taking the all-state averages (bottom line of table 1) in the applications to be discussed below. The first application is a determination of the factor Ppo/P occurring in the (p, 7) yield: Y(p, "l) = (2J + 1)P.rPpo/P. We consider resonances with known j r ; T which have not been observed in (P, P0)" At such a resonance one may first make the
bO bO --O
(keV)
(keV)
jzr; T
8036
1800 c)
1-; 0 1÷;0 1-; 1 1÷; 1
4-; 0 4-; 1
M1 IS
-2.72(30) -2.63(39) -3.00(26)
-2.64(35)
-1.92(28) -2.54(30)
-2.72(19)
-2.63(25) -3.00(17)
-2.64(22)
-2.54(19) -1.92(18)
-1.61(4) a) -2.74(13) a)
M1 IV
av E1 IS
E2IS
-4.45(19) 4.04(28)
-4.17(21)
-3.49(21) -4.31(14)
-3.29(25) -3.83(32)
-4.45(21) -4.04(31) -4.17(27)
-4.31(16) -3.49(24)
-3.83(36) -3.29(28) +0.57(61)
-3.48(6) a) -4.44(8) a) +0.10(8) a)
EIlV
+0.57(62)
-1.08(16) a)
E2IV
5.2(24) 10.1(24) 15.0(24) 16.3(24)
-2.5(28) 62.6(28)
2.1(28) 44.4(28)
-0.23(13) 20 -0.31(13) -0.56(14) -0.49(13)
30
23
X2 _ <×2>av l°g(Fp0/r) Number of transitions
T(8036) = 0 ~r(8036) = -
T(7168) = 0
T(5495) = 0
Conclusion
a) From table 1. b) For this bound state four decay branches and 19 feeding resonance primaries have been used. The measured lifetime upper limit of 35 fs could be used as a lifetime measurement. c) For this resonance I'p0 has not been measured. The (log S>av values listed, calculated under the assumption Ppo/F = 1, have then to be compared to the corresponding values from table 1 ; a least-squares calculation then yields the ratio rpo/r (column 1 1).
7168
896
5495 b) 2+;0 2+; 1
Ex
Ep
Table 2 Logarithmic 7-ray strength for an 26 A1 bound state and for two resonances.
o~
7o oo
70
t"
.<
~o
g
ra
o e-
<
Volume 173, number 3
PHYSICS LETTERS B
usual assumption Fpo/P = 1, and calculate the strengths of individual decay transitions from the measured resonance yield and branchings. If the corresponding character averages are significantly smaller than the all-state averages of table 1, the differences can be used in a least-squares calculation of log(Fpo/r' ) For six resonances I'po/[' could be determined in this way. For instance, for the Ep = 533 keV 4+; 1 resonance we find r p o / r = 0.040(17). The small value might be explained by this state being a low-lying l -- 2 resonance with a correspondingly small Coulomb barrier penetrability for the incoming proton. For 20 other resonances log(Ppo/Y ) was found to be zero within twice the error. We now turn to some other applications which are presented in table 2. The large strength differences of about an order of magnitude between isospin-allowed and isospin-retarded transitions suggest that GRSS can at least also be used to determine isospin. To the E x = 5495 keV bound state j~r = 2 + had been assigned from the present (p, 3') work combined with previous particle transfer work [2], but the isospin had remained undetermined. For the four decay transitions and the 19 resonance feeding transitions character averages are calculated which are then compared to the all-state averages from table 1. The corresponding ×2 value is compared to (X2)av (= N, with N being the number of character averages considered; the error in ×2 amounts to x/'2--N). It is seen (table 2) that for j r ; T = 2+; 0 the ×2 value is excellent, whereas the 2+; 1 possibility is clearly rejected. In the same way T = 0 has also been determined for the E x = 5007 and 5010 keV bound states, with j~r = 2 - and 1+, respectively. For the Ep = 896 keV (E x = 7168 keV) resonance, GRSS provides an equally unambiguous T = 0 determination (table 2). Analogous T-determinations could be obtained for the Ep = 1184, 1515, 1580 and 1811 keV resonances. The Ep = 1800 keV (E x = 8036 keV) resonance is a more complicated case with parity, isospin and I'po/I" as unknown parameters. The latter ratio is again treated as a multiplicative factor to be determined from a least-squares calculation as explained above. It is seen (table 2) that all possibilities are rejected but jTr ; T = 1 - ;0.
228
12 June 1986
It has been shown that GRSS has provided a considerable number o f J ~r; T determinations in 26AI. Of the 158 states below E x = 8.1 MeV the j,r ; T value is now known unambiguously for 139. In addition GRSS has yielded resonance Fpo/F values, and thus values of Pv, which has extended the number of transitions with known strength to 1940. It is not quite clear in how far the use of GRSS can be extended to other nuclei. Maybe 26A1 is just a particularly happy choice. Anyway 26A1 does not show very strong collective or single-particle transitions, which helps to provide a steep slope on the high-strength side for the strength distribution of a particular transition character. Actually it is amazing that the strengths of transitions deexciting resonances differing in (p, 3') yield by as much as a factor 4000 still cluster so closely around the averages given in table 1. This is primarily due to the fact that different resonance j,r ; T values offer very different decay possibilities. A 4+; t resonance, for example, can decay by strong high-energy M I l v transitions to the states a t E x = 0 and 417 keV with J n ; T = 5+;0 and 3+;0, respectively. On the other hand, a 6 - ; 0 resonance can only decay through weak E1 IS transitions to 5+; 0 states, or by means of still weaker low-energy E2IS transitions to 4 - ; 0 levels (with the lowest at E x = 5396 keV). Secondly, the factor Fpo/F causes yield differences of up to a factor of 25 (with an example discussed above). And finally the factor 2J + 1 in the expression for the yield can run from 1 to 13 for J = 0to J=6. This investigation was performed as part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek" (ZWO).
References [1] P.M. Endt and C. van der Leun, At. Data Nucl. Data Tables 13 (1974) 67; Nucl. Phys. A235 (1974) 27. [2] P.M. Endt and C. van der Leun,Nucl. Phys. A310 (1978) 1 [3] D.O. Boerma et al., Nucl. Phys. A449 (1986) 187. [4] G. Adams et al., J. Phys. G10 (1984) 1747. [5] H.G. Price et al., Phys. Rev. C10 (1974) 415.
PHYSICS LETTERS B
12 June 1986
G A M M A - R A Y S T R E N G T H S T A T I S T I C S APPLIED TO THE 2SMg(p, ~)Z6A! REACTION P.M. E N D T , C. A L D E R L I E S T E N
and P. D E W I T
Fysisch Laboratorium, Rijksuniversiteit Utrecht, P.O. Box 80000, 3508 TA Utrecht, The Netherlands
Received 27 February 1986
For 1250 out of 2700 y-ray transitions observed in 26A1by means of the 25Mg(p, ~)26A1 reaction the transition character (M1Ev,Mlm, Elw, Elm, E2 m or E2w, with IV and IS standing for isovector and isoscalar, respectively) and the strength (in W.u.) have been determined. The (logarithmic) average strengths for these six groups of transitions turn out to have a wide applicabilityin nuclear spectroscopy. They have been used for the determination of parities and isospins of (p, ~) resonances and bound states, and they provide a measure of Fp0/F (Fp0 ground-state proton width, F total width) for those resonances which had not been observed in previous 25Mg(p, Po) work.
The strength averages for 3,-ray transitions of the same character (split up according to multipolarity, E or M, A T = 0 or A T = 1) have almost been disregarded in nuclear spectroscopy. The use of such averages was even strongly discouraged [1] because it was argued that future more refined detection methods (more sensitive detecors, lower background etc.) would result in the detection o f many more weak transitions, thus lowering the averages. The present paper will show that y e t gamma-ray strength statistics (GRSS) can be extremely useful, provided that they are based on a large and homogeneous set o f transitions, all observed in the same nucleus with the same reaction and the same detection set-up. The set o f transitions considered here stems from the 25Mg(p, 7)26A1 reaction investigated at 75 resonances in the Ep = 0 . 3 1 - 1 . 8 4 MeV region. Spectra with good statistics (up to 3000/2Ah) have been taken with 8 0 - 1 1 0 cm 3 Ge and Ge(Li) detectors at angles of 55 ° and 90 ° to the proton beam (the 55 ° detector provided with a Compton suppression shield), for the measurement o f 3'-ray intensities and energies, respectively. Altogether 84 lower states are excited in the resonance decay. In addition about 40 resonance -+ resonance transitions were found. Many resonances and lower states had not been observed previously. Accurate energies (AE x = 3 0 - 2 0 0 eV) have been measured except for some broad resonances, and lifetimes (or lifetime limits) have been obtained for
most bound states from measured Doppler shifts. The number o f observed transitions between bound states amounts to 530 and that o f primary transitions from the resonances to 2130. For many states the abovementioned detailed spectral information combined with data from other reactions provides unambiguous assignments of spin, parity and isospin ( T - 0 or 1). In addition to the information given in the most recent A = 2 1 - 4 4 compilation [2], data from the 28Si(~, c026A1 [3] and 25Mg(p, p0)25Mg [4] reactions have been particularly useful, the former providing parities (natural or unnatural) of many bound states, whereas from the latter /-values (and thus parities) have been obtained for 39 resonances in the Ep = 0 . 8 0 - 1 . 8 4 MeV region. We now have resonances with 22 different J r r ; T assignments (J = 1 - 5 with 7r = +, T = 0 and T = 1, two 6 - ;0 resonances and a probable 0 - ; 0 resonance). The "),-ray based j~r ; T assignments (or limitations) make use of recommended upper limits (RUL's) for 3,-ray strengths, defined in ref. [ 1 ]. F r o m the present very large set o f transitions in 26A1 (many more than the 950 transitions between bound states in the whole A = 6 - 4 4 region discussed in ref. [1 ]) upper limits have been derived for some important transition characters (for use in 26A1 only). They are 0.002, 0.05, 5 and 50 W.u. for Ells, M i l s , E21V and E2IS , respectively, to be compared to 0.003, 0.03, 10 and 100 W.u. in ref. [1]. The differences are seen to be at most 225
Volume 173, number 3
PHYSICS LETTERS B
Oh
o~ I~
g,
ee~
¢.q
g
m~ i
I
< ~a O II
g
g ~q
e~4
t--- I
g eq
~D
oO
eq
mel
g.
I
,-;,
g
Paa,
~,-g
eq <-,i
-g O
_o g ea
+g O
t •
226
O
12 J u n e 1 9 8 6
a factor of 2. No M2 transitions (only five are observed) or transitions of higher multipolarity are considered in the present paper; almost any such transition exceeding the detection limit would exceed the corresponding RUL's set in ref. [1]. Strength averages for 1249 transitions proceeding between states with known j,r ; T are given in table 1. None of these transitions exceed the upper limits mentioned above. All transitions are considered to be unmixed (8 = 0). From previous work [2] the mixing ratios are known of only nine transitions between bound states, and the present work has not offered any new information (angular distribution measurements have not been performed). Resonances were only taken for which P p o / P had been measured, mostly from (p, P0) [4], and which could be considered as virtually isospin-pure. The most sensitive measure of T-purity is the strength average for M I I s and/or E1 IS. A significant excess of these averages over the bound-state averages points to T-mixing A very clear case of T-mixing is offered by the pair resonances at Ep = 1205 and 1237 keV, both with j,r = 3 +. The 45-branch decay is almost identical, and the M I l v and M I I s averages are equal to within the combined error. Another 8 resonances were also rejected because of considerable T-mixing with strong resonances with the same jTr in the neighbourhood. The strength distributions for different transition character have rather different widths. The RMS logarithmic deviation from the average for a single transition amounts to A log S = 0.79, 0.50, 0.56, 0.63, 0.86 and 0.88 for M I l v , MIls, E I I v , Ells, E2ts and E2IV, respectively. A comparison of the bound -+ bound and resonance -+ bound averages in table 1 shows that for all transition characters the averages are equal within twice the combined error except for M I I s . Apparently some of the resonances taken still contain weak T-admixtures. The differences are not considered large enough, however, to prevent us from taking the all-state averages (bottom line of table 1) in the applications to be discussed below. The first application is a determination of the factor Ppo/P occurring in the (p, 7) yield: Y(p, "l) = (2J + 1)P.rPpo/P. We consider resonances with known j r ; T which have not been observed in (P, P0)" At such a resonance one may first make the
bO bO --O
(keV)
(keV)
jzr; T
8036
1800 c)
1-; 0 1÷;0 1-; 1 1÷; 1
4-; 0 4-; 1
M1 IS
-2.72(30) -2.63(39) -3.00(26)
-2.64(35)
-1.92(28) -2.54(30)
-2.72(19)
-2.63(25) -3.00(17)
-2.64(22)
-2.54(19) -1.92(18)
-1.61(4) a) -2.74(13) a)
M1 IV
E2IS
-4.45(19) 4.04(28)
-4.17(21)
-3.49(21) -4.31(14)
-3.29(25) -3.83(32)
-4.45(21) -4.04(31) -4.17(27)
-4.31(16) -3.49(24)
-3.83(36) -3.29(28) +0.57(61)
-3.48(6) a) -4.44(8) a) +0.10(8) a)
EIlV
+0.57(62)
-1.08(16) a)
E2IV
5.2(24) 10.1(24) 15.0(24) 16.3(24)
-2.5(28) 62.6(28)
2.1(28) 44.4(28)
-0.23(13) 20 -0.31(13) -0.56(14) -0.49(13)
30
23
X2 _ <×2>av l°g(Fp0/r) Number of transitions
T(8036) = 0 ~r(8036) = -
T(7168) = 0
T(5495) = 0
Conclusion
a) From table 1. b) For this bound state four decay branches and 19 feeding resonance primaries have been used. The measured lifetime upper limit of 35 fs could be used as a lifetime measurement. c) For this resonance I'p0 has not been measured. The (log S>av values listed, calculated under the assumption Ppo/F = 1, have then to be compared to the corresponding values from table 1 ; a least-squares calculation then yields the ratio rpo/r (column 1 1).
7168
896
5495 b) 2+;0 2+; 1
Ex
Ep
Table 2 Logarithmic 7-ray strength for an 26 A1 bound state and for two resonances.
o~
7o oo
70
t"
.<
~o
g
ra
o e-
<
Volume 173, number 3
PHYSICS LETTERS B
usual assumption Fpo/P = 1, and calculate the strengths of individual decay transitions from the measured resonance yield and branchings. If the corresponding character averages are significantly smaller than the all-state averages of table 1, the differences can be used in a least-squares calculation of log(Fpo/r' ) For six resonances I'po/[' could be determined in this way. For instance, for the Ep = 533 keV 4+; 1 resonance we find r p o / r = 0.040(17). The small value might be explained by this state being a low-lying l -- 2 resonance with a correspondingly small Coulomb barrier penetrability for the incoming proton. For 20 other resonances log(Ppo/Y ) was found to be zero within twice the error. We now turn to some other applications which are presented in table 2. The large strength differences of about an order of magnitude between isospin-allowed and isospin-retarded transitions suggest that GRSS can at least also be used to determine isospin. To the E x = 5495 keV bound state j~r = 2 + had been assigned from the present (p, 3') work combined with previous particle transfer work [2], but the isospin had remained undetermined. For the four decay transitions and the 19 resonance feeding transitions character averages are calculated which are then compared to the all-state averages from table 1. The corresponding ×2 value is compared to (X2)av (= N, with N being the number of character averages considered; the error in ×2 amounts to x/'2--N). It is seen (table 2) that for j r ; T = 2+; 0 the ×2 value is excellent, whereas the 2+; 1 possibility is clearly rejected. In the same way T = 0 has also been determined for the E x = 5007 and 5010 keV bound states, with j~r = 2 - and 1+, respectively. For the Ep = 896 keV (E x = 7168 keV) resonance, GRSS provides an equally unambiguous T = 0 determination (table 2). Analogous T-determinations could be obtained for the Ep = 1184, 1515, 1580 and 1811 keV resonances. The Ep = 1800 keV (E x = 8036 keV) resonance is a more complicated case with parity, isospin and I'po/I" as unknown parameters. The latter ratio is again treated as a multiplicative factor to be determined from a least-squares calculation as explained above. It is seen (table 2) that all possibilities are rejected but jTr ; T = 1 - ;0.
228
12 June 1986
It has been shown that GRSS has provided a considerable number o f J ~r; T determinations in 26AI. Of the 158 states below E x = 8.1 MeV the j,r ; T value is now known unambiguously for 139. In addition GRSS has yielded resonance Fpo/F values, and thus values of Pv, which has extended the number of transitions with known strength to 1940. It is not quite clear in how far the use of GRSS can be extended to other nuclei. Maybe 26A1 is just a particularly happy choice. Anyway 26A1 does not show very strong collective or single-particle transitions, which helps to provide a steep slope on the high-strength side for the strength distribution of a particular transition character. Actually it is amazing that the strengths of transitions deexciting resonances differing in (p, 3') yield by as much as a factor 4000 still cluster so closely around the averages given in table 1. This is primarily due to the fact that different resonance j,r ; T values offer very different decay possibilities. A 4+; t resonance, for example, can decay by strong high-energy M I l v transitions to the states a t E x = 0 and 417 keV with J n ; T = 5+;0 and 3+;0, respectively. On the other hand, a 6 - ; 0 resonance can only decay through weak E1 IS transitions to 5+; 0 states, or by means of still weaker low-energy E2IS transitions to 4 - ; 0 levels (with the lowest at E x = 5396 keV). Secondly, the factor Fpo/F causes yield differences of up to a factor of 25 (with an example discussed above). And finally the factor 2J + 1 in the expression for the yield can run from 1 to 13 for J = 0to J=6. This investigation was performed as part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materie" (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek" (ZWO).
References [1] P.M. Endt and C. van der Leun, At. Data Nucl. Data Tables 13 (1974) 67; Nucl. Phys. A235 (1974) 27. [2] P.M. Endt and C. van der Leun,Nucl. Phys. A310 (1978) 1 [3] D.O. Boerma et al., Nucl. Phys. A449 (1986) 187. [4] G. Adams et al., J. Phys. G10 (1984) 1747. [5] H.G. Price et al., Phys. Rev. C10 (1974) 415.