AGS CNI Update: Non-linear Corrections to Energy Loss in Si Dead Layer Outline Standard dead layer fitting technique Non-linear corrections Compare results of the two methods

Calculating Energy Loss Generate dE/dx as a function of carbon energy (E kin ) from MSTAR ver 2.00 Calculate energy loss tables for 150 < E kin < 2000 keV for dead layer thicknesses 20 < t dead < 100  g/cm 2 Carbon Energy (keV) dE/dx (keV cm 2 /  g)

Standard Technique Fit linear correlation b/w E kin and E dep for 400 < E kin < 800 keV E kin = A + B E dep B  1  A  E dead Fit Slope (B) as linear function of E dead (A) Slope = a + b E dead E kin = E dead + (a + b E dead ) E dep E dep E kin

Non-Linear Corrections Fit E kin to E dep correlation for different t dead E kin = P 0 + P 1 E dep + P 2 (E dep ) 2 + P 3 (E dep ) 3 + P 4 (E dep ) 4 P n (t dead ) depend on dead layer thickness Fit P n (t dead ) with 3 rd order polynomial P n (t dead ) = C n,0 + C n,1 t dead + C n,2 (t dead ) 2 + C n,3 (t dead ) 3 Now have 20 parameters rather than 2

Non-Linear Correction Results Extract T0 and t dead (E dead ) From TOF to E kin correlation First data set March 13 – standard fit –E dead = 70.6 keV  t dead  21  g/cm 2 –T0 = 27.7 ns March 23 – non-linear fit –t dead = 34.2  g/cm 2 –T0 = 26.4 ns Second data set April 1 – standard fit –E dead = 63.4 keV  t dead  19  g/cm 2 –T0 = 34.4 ns April 1 – non-linear fit –t dead = 31.2  g/cm 2 –T0 = 34.5 ns

Correction Effect on Polarization First data set March 13 – standard fit = 1.28% March 23 – non-linear fit = 1.26% Second data set April 1 – standard fit = 1.29% April 1 – non-linear fit = 1.28% (P non-linear – P standard ) / P standard April 1 data