NEUTRON POLARIZATION ANALYSIS FOR n+p _ d+γ Monisha Sharma

Transcription

1 NEURON OLARIZAION ANALYSIS FOR n+p _ d+γ Monisha Sharma he neutron spin filter and neutron polarization of the LANSCE npdgamma experiment have been studied. A detailed description of the analysis and its short comings is provided. He polarization of nearly % percent has been measured, but the polarization varied significantly during January-August of. olarized He as spin filters. olarized He spin filters are based on the spin dependence of the He- neutron capture cross section. For the He spin parallel to the neutron spin the neutron capture cross section is essentially zero, whereas for the anti parallel spins, the capture cross section is ±7 barns at. mev. All other channels have comparatively small cross sections at thermal energies. heory for the analysis: he transmission for unpolarized neutrons with spins parallel and antiparallel to the He spin, on an ensemble of polarized He nuclei with polarization He is given by, t ± = exp( nlσ ( m He ) ) where n is the He number density, l is the length of the sample and σ is the cross section for unpolarized neutrons incident on unpolarized He. olarization of the transmitted beam, n, is then, t + t n = = tanh( nlσ t + t + He ) he transmission through the filter is given by ( t + + t ) = exp( nlσ ) Cosh( nlσ He ) And the beam polarization is given by, = ( / ) = tanh( nlσ n He )

2 Experimental Set Up : F- (_) Flipp er Experiment A(_) M M M Fig. : Experimental set up Analysis: Analysis is done for the data for the month of January through August. Data is collected by monitors M and M for different set ups (when He cell is polarized, when the cell is unpolarized, when silicon wafers are in between M and M, and pedestal runs). For each polarization run, two adjacent pedestal runs are combined with and Si runs to determine the neutron polarization. OF is converted to wavelength: Since the positions of M and M are different, a given time of flight corresponds to a different wavelength/velocity. ime of flight is converted to wavelength for both M and M, and the M data are interpolated to the wavelength at M as follows: Distance of monitor from the moderator =.7 m Distance between monitor and monitor =. m Distance between monitor and monitor =.7 m All these distances are measured using a tape ( from David Bowman dated /9/). he time of flight is converted to wavelength using the de Broglie wavelength equation h h * tof tof = = =.9 * mv md d where tof is the time of flight and d is the distance of each monitor from the source. We allow for an overall offset in the time (i.e. tof real time of flight) later in the analysis. Interpolation of m to m: As the time required by the neutrons to reach different monitors is different and therefore different wavelengths, we interpolate the data from one monitor w.r.t the other monitor to obtain the data at the same wavelength for the two monitors. herefore, data from monitor is linearly interpolated to the data obtained at monitor M, i.e.,

3 int ( M [ i + ] M [ i]) M [ i] = * ( [ i] [ i]) + M [ i] [ i + ] [ i] where and are the wavelengths at monitor and monitor respectively, and the index i labels the discrete time of flight bin. For each polarized run, the analysis requires one unpolarized run, one run with silicon wafers in between the monitors, one polarized run and two pedestal runs, one before and one after the polarized run to get a better correction for the background. he two pedestal runs are averaged (Moffs and Moffs) to determine a constant, which is subtracted from the actual data to M and M respectively. Dependence of Si on wavelength: M SiInt M offs he transmission through the Silicon wafers (and air), Si =, has a MSiInt Moffs dependence on wavelength, most likely due to He in monitors. his can be seen clearly in the plot shown in Fig.. Fitting this to an exponential yields and assuming it is He, gives a thickness nl.7 bar-cm ( bar ~.8x 9 cm - ). and an attenuation of % at Å. Also, the Bragg peaks due to the Al windows of the monitors (downstream in M and upstream in M) can be seen in the plot..9 Si Wavelength (Å) Fig. : Si vs wavelength his wavelength dependence of transmission is included in our analysis.

4 Equations used in the analysis: M ol M offs M Unpol M offs = Mol Moffs MUnpol int Moffs M Unpol M offs = MUnpol Moffs M SiInt MSiInt Si M offs M offs n = ( ) Si M ol M offs = Mol Moffs M SiInt MSiInt M offs Moffs Here the pedestal run averages, Moffs and Moffs, are constants for each run. Method I In Method I, / Si and / are used and are separately fit to functions of () to extract the He thickness and for each run. he plots of / Si and / for the January analysis are shown in Fig.. / Si x - / x wavelength (Å) Wavelength (Å) Fig. : ()/ Si () and ()/ () vs wavelength

5 () / Si () vs is fit to the exponential function, A * exp( α * ) where, α = nlσ And ()/ () vs wavelength is fit to the function, Cosh( β * ( offs )) where offs an offset that can account for t drift, and nlσ β = He He polarization is given by, He = β / α. he He polarization derived from best fit values of α and β is very stable to changes in the fit range indicating that the background and related effects do not affect the value of He at much better than the % level. he He thickness is given by nl=.8*.98α.7 bar-cm. ransmission of neutrons through the glass is given by the constant A. (A weak wavelength dependence of glass transmission was observed in a study with pieces of GE-8 glass has been reported to. Gentile by D. Bowman.) he neutron polarization derived from ()/ () is shown in fig.. Neutron olarization, n x - Wavelength (Å) Fig. : Neutron olarization vs wavelength his can also be fit to tanh( β * ( )) to determine β, and = β / α offs his is not, in principle, and independent measure of the neutron or He polarization, and the He polarization is quite consistent. He

6 Method II ( ) We expect = exp( nlσ ) Cosh( nlσ He ) and we could, in principle use the Si( ) ratio to determine and α separately without the data; however this form reduces to a double exponential, which can be very unstable to least squares fitting (non-orthogonal chi- space). We have not had much success with this approach. ests of our fitting program with simulated data confirmed that problems could be expected. Nevertheless, here s a sample: /Si x - Wavelength (Å) he fitting function used for this plot is, Fig. : / Si vs wavelength A* exp( α) * Cosh( α * olarization * ( offs )) where olarization gives the He polarization and A gives the transmission through the cell. For January runs, the polarization obtained by this method is between % to % for any fit range. Simulated data: Simulated M data were generated by using the signal (i.e. data) from M and propagating through windows and polarized and unpolarized He as follows: munpolcalc = ( MUnpol Moffs) *.7 *exp(.8* ) + M offs.8* m polcalc = ( Mol Moffs) *.7 * exp(.8 ) * Cosh(.8 *.8) + moffs.8 * he last term (.8 ) is an ansatz background term discussed below. Figure shows / from real data (a.) and simulated data (b.). he experimental data show a systematic variation of the residuals. his could be due to background in M that does not reach M. When this is added to the simulated data (the.8 term), similar

7 residuals are found in M (graph on the right). his extra M signal is consistent with wrap-around neutrons, slow neutrons from the penultimate pulse, which are strongly attenuated in the He spin filter cell, and do not reach M significantly x x - olratio olratiocalc Wavelength Wavelength (a) (b) Fig. : (a)graph from experimental data, (b)graph from Simulated data Background issues: In addition to the background which, is measured without the neutron shutter closed, there are other sources of background counts. here are wrap around neutrons from the previous pulse not eliminated by the chopper. Also, there is scattering of neutrons from the monitors, shielding etc. We need to take care of these wrap around neutrons and other contributions to the background to get the polarization measurement to higher accuracy. Results: From the above mentioned analysis, the following results were obtained for the January run. For Method I, the errors assigned represent the variations observed when the fit range was changed. For Method II, a reasonable, but somewhat arbitrary range was selected. hickness Glass e He olarization Neutron (bar-cm) olarization(atå) Method I.7±..8±..78±..79±. Method II

8 he graph for olarization vs time (over a period of 8 months) is shown in fig olarisation..... // // 7// Date Fig. 7: He olarization vs time Conclusions: olarisation for the month of January was around 8%, February was around % but for the month of March the polarization was around %. In June, the polarization was around 9% and in August it was around %. he data for May is also analyzed and it is observed that, till May th polarization was around 8% but after that it dropped to around %. From the analysis of January data, it is seen that we are able to attain a maximum neutron polarization of 79.% at a wavelength of Å. he observed polarization instabilities have not been clarified, though it is agreed that more laser power would make the experiment less susceptible to changes in the optics, cell conditions, etc. 8