Measurement of the ratio (π−3He → π0t)(π−3He → dn) and of the respective partial K X-ray yields

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<ul><li><p>Nuclear Physics A448 (1986) 567-577 @ North-Holland Publishing Company </p><p>MEASUREMENT OF THE RATIO (n- 3He + nt)/( mr- 3He + dn) </p><p>AND OF THE RESPECTIVE PARTIAL K X-RAY YIELDS </p><p>Cl. BACKENSTOSS, M. IiYCKI, W. KOWALD, P. WEBER and H.J. WEYER </p><p>Institute for Physics, University of Basel, Basel, Switzerland </p><p>S. LJUNGFELT, U. MANKIN, G. SCHMIDT and H. ULLRICH </p><p>Kernforschungszentrum Karlsruhe, Institut fir Kemphysik und Universitiit Karlsruhe, Karlsruhe, Fed. Rep. of Germany </p><p>Received 8 August 1985 </p><p>Abstract: The reactions rr- He + rrt and r- 3 He + dn have been measured for stopped pions. The ratio (P- He+ &amp;)/(~~3He-t dn) was determined to be 1.15k0.12. In addition the pionic K X-rays were measured in coincidence for both reaction channels resulting in K X-ray yields of YE,= (35 i 4)% and Y, = (45 f 5)% respectively. Using also i-stilts from previous measurements, branch- ing ratios per stopped pion for all absorptive channels as well as their absolute 1s rates were determined. </p><p>NUCLEAR REACTIONS3He( r-, PO), ( mr-, d), E at rest; measured reaction rates, (particle) (pionic X-ray)-coin; deduced branching ratios, partial K X-ray yields. </p><p>1. Introduction </p><p>Pion absorption in 3He has received considerable experimental and theoretical </p><p>interest. This nucleus bridges the gap between deuterium, where most studies on </p><p>pion interactions have been performed, and all other nuclei. Since 3He is a relatively </p><p>simple nucleus it allows kinematically complete experiments and serves as traditional </p><p>testing ground for various theoretical approaches as well. </p><p>In the present paper we report on results from studies with pions at rest. In this </p><p>case two more arguments for the importance of such studies can be added: (i) 3He </p><p>is the only nucleus besides hydrogen where the charge-exchange channel (CEX) is </p><p>already open for pions at rest and a Panofsky ratio can be measured. (ii) We have </p><p>one of the rare occasions to study s-wave pion interaction, since absorption in flight </p><p>favours p-waves and also for absorption at rest in somewhat heavier nuclei higher </p><p>I-values dominate by far. </p><p>Even in 3He, pion interactions at rest contain p-wave contributions which cannot </p><p>be neglected a priori. They can, however, be separated by a special experimental </p><p>method. In this method the reaction products are observed in coincidence with a </p><p>pionic K X-ray, which confirms that the pion was interacting from the 1s orbit. </p><p>Experimental investigations with pions at rest have the intrinsic difficulty to </p><p>determine the absolute number of pions stopped in the target. This problem is even </p><p>567 </p></li><li><p>568 G. Backenstoss et al. / T- 3 He + w0 t, dn </p><p>more severe with a large target volume as required for gaseous materials. Con- </p><p>sequently the branching ratios for specific reaction channels in 3He which can be </p><p>found in literature exhibit quite large discrepancies. Therefore, in our experimental </p><p>program we have measured different reaction channels in parallel and thus deter- </p><p>mined their ratios. The sum of all absorptive events (including charge exchange </p><p>and radiative capture) is equal to the number of stopped pions. The present paper </p><p>completes this series of measurements lm3) with results from the charge exchange </p><p>reaction, normalized to the dn reaction which has been measured in parallel. Only </p><p>for the relatively weak radiative channel results from other groups 4*5) have been used. </p><p>In addition, the K X-ray yield for the charge-exchange reaction has been deter- </p><p>mined. This completes also a series of measurements of partial K-yields6*) for </p><p>different reaction channels and allows now to disentangle the pion capture process </p><p>at rest in 3He completely. </p><p>2. Experiment and data analysis </p><p>The experiment was performed at the nE1 channel of the SIN ring accelerator </p><p>with the setup shown in fig. 1. Negative pions were degraded by graphite and </p><p>stopped in a 12 cm long, 6 cm diameter gaseous 3He target covered by thin mylar </p><p>foils. The gas was cooled down by liquid 4He to about 5 K, resulting in a density </p><p>of 80 mg/cm2. </p><p>Two gammas from the no decay were detected in coincidence by two large NaI </p><p>counters Nail and Na12, 27.5 cm and 21 cm in diameter and 28 cm and 27.5 cm </p><p>thick, positioned 99.7 cm and 101.3 cm from the target, respectively. The angle </p><p>between the axes of Nail and Na12 was 155.6, which is close to the minimum </p><p>angle 0min = 152.8 [COS emin= 1 -2(m,o/EFA)2; EzA= 138.85 MeV]. </p><p>In front of both NaI detectors, thin plastic anticoincidence counters were placed, </p><p>allowing software rejection of events with charged particles. The acceptance for the </p><p>ire detection via the 2 y decay depends critically on the geometry of Nail and Na12 </p><p>and has been calculated with a Monte Carlo program described below. Simul- </p><p>taneously with the r gammas, monoenergeticdeuterons from the dn channel were </p><p>detected by a total absorbing counter consisting of two identical plastic scintillators </p><p>with a 17 x 17 cm2 surface and 8 cm thick. Placed at a distance of 82 cm from the </p><p>target, the counter covered a total solid angle of 0.085 sr and had an energy resolution </p><p>of 7% for 36 MeV protons. Between counter and target a thin dE/dx counter was </p><p>mounted for particle identification. </p><p>In order to detect pionic X-rays four thin NaI detectors (0.1 mm thick, 4.54 cm </p><p>active diameter) were placed 12 cm below the target. The total solid angle was </p><p>0.44 sr. By counting the number of X-rays, observed in coincidence with deuterons </p><p>and two gammas respectively, the partial K-yield of these two reaction channels </p><p>could be determined. </p><p>The data analysis has been made as follows: </p></li><li><p>G. Backenstoss et al. / vr He + rot, dn 569 </p><p>D: Degrader T :gaseous 3He-Target S;dE/dx-counter E: total absorbing counter </p><p>si- </p><p>A:anticounter T, 2 3 ,+:telescope counter </p><p>3 , , </p><p>! </p><p>Target enlarged with 4NaI </p><p>Fig. 1. Setup with Nall, Na12 and the total absorbing scintillation counter; drawn enlarged are the four thin NaI detectors which were installed below the target. </p><p>GT analysis. For Nail and Na12, pulse heights as well as times of flight were recorded. As an example the measured distributions from Nail are shown in fig. </p><p>2. For r identification, an event is required to fall into the peak of both </p><p>time-of-flight distributions and to exceed the pulse-height thresholds of 20 MeV and </p><p>25 MeV for Nail and NaI2. The number of TOS originating in the target walls was </p><p>determined in a separate measurement with an empty target and subtracted accord- </p><p>ingly. This contribution turned out to be a few percent of the full target effect only. </p><p>The relevant numbers are given in table 1. </p><p>The calculation of the rr acceptance, based on the Monte Carlo method, was </p><p>done in two steps: First, the y-efficiency was calculated by simulating the electron ) </p><p>shower development with the Monte Carlo program EGS for about 1000 </p><p>sets of 4 parameters describing the -y-ray in our experiment. These parameters are </p><p>the y-energy (53.1 MeVS E, s 85.7 MeV) and 3 geometrical parameters describing </p><p>the y-ray intersecting with the NaI detector (the distance r of the intersection point </p><p>on the surface of the NaI to its centre and the polar angles 0 and 4). In the second </p><p>step, values for the 4 parameters of the ys from simulated ?r decays were generated </p></li><li><p>570 G. Backenstoss et al. / T- jHe + n-Or, dn </p><p>dN boo_ dE </p><p>20 MeV threshold b) </p><p>loo_ ENERGY </p><p>I I I I I 20 LO 60 60 lOO[MeV] </p><p>Fig. 2. (a) Time spectrum of the ys from the r+2y decay as registered in Nail. The time zero is given by the accelerator r.f. (b) Energy spectrum of coincident y-rays from r+ 2y decay detected in Nall. </p><p>TABLE 1 </p><p>Data determining R = N( 6 3He + pot)/ N( wiT He + dn) </p><p>Corrections Data </p><p>deuterons : Nd acceptance NJtot) = N,4n/a </p><p>PO mesons: full target: N,n empty target: N,e measuring time: full/empty </p><p>N,o-o,N,o correction due to r + ye+e-: N,,o=5010/(1-p) acceptance and efficiency: N,o(tot) = N-01 y </p><p>(1 = 0.085 sr (1.06i0.03)x105 </p><p>(1.57 f 0.05) x 10 </p><p>(5.30*0.25)x lo3 s5*15 </p><p>a, = 3.4 (5.01 f 0.26) x lo3 </p><p>p = 1.2% (5.07ztO.26) x lo3 </p><p>y = (2.8 * 0.25) x 10m4 (1.81*0.15)x 10 R = 1.15*0.12 </p><p>by another Monte Carlo program and for each 7~ decay the efficiency was determined by means of a fourfold interpolation between values stored as a result of the first </p><p>step. In order to account for the extended target, the Monte Carlo simulations were done for several target coordinates and the resulting values were weighted with the </p><p>pion stop distribution. A small correction was further applied taking into account </p></li><li><p>G. Backenstoss et al. / T- 3 He + not, dn 571 </p><p>the fraction of TOS decaying into ye+e-, which are missed in our r trigger (see </p><p>table 1). </p><p>d-analysis. For charged particles, a coincidence of counters S and E (see fig. 1) </p><p>was required. Deuterons were separated from other charged particles by a combina- </p><p>tion of pulse-height and time-of-flight information. The energy distribution of the </p><p>deuterons is shown in fig. 3. It shows a rather flat distribution of background </p><p>deuterons originating from the target walls superimposed by a pronounced peak </p><p>from the monoenergetic deuterons from 3He. The latter can be fitted very well by </p><p>a gaussian distribution. Its area determines the number of good events. The respec- </p><p>tive numbers are also given in table 1. </p><p>Fig. 3. Energy spectrum of the deuterons with gaussian fit. </p><p>As result of table 1 we find for the ratio of CEX to the dn reaction </p><p>R = 1.15*0.12. the value </p><p>X-ray analysis. The number of K X-rays observed determines the fraction of </p><p>events originating from the 1s orbit. Measured X-ray spectra are given in fig. 4. Fig. </p><p>4b (dotted curve) shows the spectrum obtained with the no trigger. CEX with </p><p>stopped pions is only possible in 3He and in H (mylar foils). The latter contribution, </p><p>however, is small (see table 1) and produces X-rays with energies too low to be detected in our apparatus. Also chance coincidences are suppressed very effectively </p><p>by the threefold coincidence condition (NaII x Na12 x small NaI). Hence the spec- </p><p>trum with the no trigger is essentially background-free. </p><p>The situation is more complicated for the deuterons where the background </p><p>contribution (smooth distribution in fig. 3) is not negligible. Consequently, also in </p><p>the corresponding X-ray spectrum (fig. 4a) lines from carbon and oxygen are </p></li><li><p>572 </p><p>Fig. also </p><p>ENERGY </p><p>I I I I I I 5 10 15 20 25 30 [keV] </p><p>dN </p><p>60_ dE </p><p>b) </p><p>-x-3He-dn </p><p>w-m__ ._j-i-3He_~0t </p><p>ENERGY </p><p>I I I I I 5 10 15 20 25 3b [keV] </p><p>4. (a) X-ray spectrum triggered by the full deuteron spectrum of fig. 3. Besides the pionic He lines, lines from *C and I60 are indicated. (b) Full line: Same as (I), but for deuterons with 35 MeVc T,s </p><p>55 MeV only. Dotted line: X-ray spectrum obtained with the P trigger. </p></li><li><p>G. Bockenstoss et al. / mm 3He + rrt, dn 573 </p><p>indicated. In order to subtract this background a window around the monoenergetic </p><p>peak in fig. 3 with 35 MeVc Td s 55 MeV has been applied. Events inside this </p><p>window contain only little background equivalent to the pedestal below the peak. </p><p>The X-ray spectrum corresponding to the window is shown in fig. 4b (solid line). </p><p>In this spectrum the remaining small background distribution from the pedestal has </p><p>been assumed to have the same shape as the X-ray spectrum from events outside </p><p>the window and has been subtracted accordingly. </p><p>The number of X-ray coincidences is given in table 2, together with the efficiency </p><p>and the correction for absorption in the material between target and X-ray detector </p><p>and the geometrical acceptance. Because of the large target extension the acceptance </p><p>has been calculated by a Monte Carlo method. </p><p>TABLE 2 </p><p>Data determining the partial K-yields Yr </p><p>Corrections Data </p><p>absorption x efficiency acceptance (i) N$ </p><p>N&gt; x ~~T/(YE = N;o(tot) (ii) NF </p><p>N, x 4rr/u = N,K(tot) </p><p>B = 0.655 f 0.025 u = 0.44 f 0.02 sr </p><p>125*12 (5.45 i 0.62) x IO3 </p><p>547 * 50 (23.85 +2.60)x lo- </p><p>Y&gt; = N:o(tot)/ N,o = 5450/ 15 500 (35 * 4)% Y, = N:(tot)/ Nd = 23 850/53 000 b, (45 f 5)% </p><p>) Based on data more extended than in table 1. b, YF was evaluated in only one of the two totally absorbing counters. Nd of table 1 is </p><p>divided by two. </p><p>3. Discussion of results </p><p>Total branching ratios. In order to determine the branching ratios ni per stopped pion we use the following relation which includes all absorptive channels: </p><p>We normalize to the dn channel since this two-particle finai state shows experi- </p><p>mentally the clearest signature. </p><p>Inserting at the left side of this equation results from our previous measurements+ </p><p>and from the present paper and at the right side the sum of yields of all radiative </p><p>+ The result for npnn/ndn has been obtained with the old data from ref. ) using an improved efficiency code for the neutron detector 9). </p></li><li><p>574 G. Backenstoss et al. / 6 3 He + rrt, dn </p><p>channels from ref. ) we find </p><p>Solving this for ndn gives </p><p>n &amp;= (11.7* 1.8)% . </p><p>Since n, * 1, it follows from the above equation that ndn depends only weakly on </p><p>n, The use of the result from ref. ) would change ndn by only a of the given error. </p><p>With the known ratios of yields the branching ratios per stopped pion can now </p><p>easily be calculated. The results are shown in table 3 together with results from </p><p>other groups. According to this table the ndn values to be found in literature are somewhat too high. This may be due to the difficulties in the proton/deuteron </p><p>separation at low energies in the early cloud-chamber work of ref. ). This suggestion </p><p>is supported by the fact that the sum of the yields npnn+ ndn of this reference agrees </p><p>quite well with our sum. Also our 7r yield is in excellent agreement with a recent </p><p>result of Bannikov et al. lo). </p><p>TABLE 3 </p><p>Observed branching ratios per stopped pion and comparison with results from other authors </p><p>%n 11.7* 1.8 15.9 f 1.6 ) 15.9 f 2.3 b, npnn 60.8 * 4.0 57.8 f 5.4 b) ndn + npnn 72.5 f 4.2 73.7 f 5.9 b) 68.2 f 2.6 d, n,o 13.5 f 2.3 12.8i1.2) 15.8 f 0.8 d, 17.8 f 2.3 d, % 14.0* 1.3 d) 10.5 f 1.3 y* </p><p>Note that our results and those from refs. ,) have been obtained with gaseous He, whereas ref. 4, used a liquid target. </p><p>* This value does not include the ypnn final state. ) Ref. I). ) Ref. 5). ) Ref. lo). d, Ref. 4). </p><p>Is rates. Most calculations for pions stopped in 3He have been made for 1s </p><p>absorption only. Since the contributions from other atomic orbits could only be </p><p>guessed, comparisons with experimental values containing all pionic transitions </p><p>were problematic. Our K-yields combined with the results of table 3 and the measured </p><p>total 1s width *) (r&amp;Is) = 28*7 eV) allow to derive absolute 1s rates. They are given in table 4 and can be compared directly with theoretical calculations for the </p><p>first time. </p><p>As an example our no rate can be compared with calculations on the basis of impulse approximation using pion-nucleon isospin 1 and $ scattering lengths. This </p><p>method has been used by several authors 13-15) and gives ng( 1s) = 9.34 x 1015 s-l. It </p><p>has been criticized by Lohs r6), who applied a multiple scattering formalism and </p></li><li><p>G. Backenstoss et al. / K He + not, dn </p><p>TABLE 4 </p><p>Compilation of Is res...</p></li></ul>