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accelerator/notes

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+notes:
+
+from program Sim NRA
+
+kinematic factor @ 2.000 ±0.001 MeV
+
+150 degrees
+
+    Cu: 1885.05 ± 0.01
+    Si: 1749.21 ± 0.01
+
+
+
+can find a ratio between the lithium and flourine cross-sections
+
+    taking the ratio of the yields and cross-sections allows things like target thickness to drop out
+
+what you're after: the yield and the cross-section are basically proportional to each other
+
+in lab write-up
+
+
+
+A big danger:
+
+    Flourine curve very sensitive to different in energy of about .1, so this could change your ratio greatly
+    this would be a systematic error that caused an energy shift to explain wrong values
+
+    

notes.R

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+plot(y,xlab="Channel",ylab="Count",lwd=4,pch="-")
+lines(v[3]*exp(-1/2*(x-v[1])^2/v[2]^2),col=2,lwd=1.4)
+abline(v = 7813.63,col=4,lwd=1)
+axis(3,at=7813.63,"5.486 MeV")
+dev.print(pdf,"../report/calibration.pdf")
+
+
+Alpha Activity
+plot(data_4_2,xlab="Energy [MeV]",ylab="Count [Alpha Particles]",pch=".")
+minor.tick(nx=5,ny=2)
+abline(v = 5.631,col=2,lwd=1)
+axis(3,at=5.631,"5.6")
+abline(v = 5.323,col=2,lwd=1)
+axis(3,at=5.323,"5.3")
+dev.print(pdf,"../report/activity.pdf")
+
+
+
+For Gaussian Fits:
+
+─────────────
+
+x <- seq_along(y)
+
+f <- function(par)
+{
+    m <- par[1]
+    sd <- par[2]
+    k <- par[3]
+    rhat <- k * exp(-0.5 * ((x - m)/sd)^2)
+    sum((y - rhat)^2)
+}
+
+optim(c(15, 2, 1), f, method="BFGS", control=list(reltol=1e-9))
+
+─────────────
+
+I propose to use non-linear least squares for this analysis.
+
+# First present the data in a data-frame
+tab <- data.frame(x=seq_along(y), y=y)
+#Apply function nls
+(res <- nls( y ~ k*exp(-1/2*(x-mu)^2/sigma^2), start=c(mu=7500,sigma=50,k=1) , data = tab))
+
+And from the output, I was able to obtain the following fitted "Gaussian curve":
+
+v <- summary(res)$parameters[,"Estimate"]
+plot(y~x, data=tab)
+plot(function(x) v[3]*exp(-1/2*(x-v[1])^2/v[2]^2),col=2,add=T,xlim=range(tab$x) )
+
+
+
+
+
+
+
+Mirror Gumbel Distribution:
+
+
+(res <- nls( y ~ (1/beta)*exp((x-alpha)/beta - exp((x - alpha)/beta)), data=cal,start=c(alpha=7800,beta=1),control=list(minFactor=1/50000,maxiter=1000)))
+v <- summary(res)$parameters[,"Estimate"]
+plot(function(x) (1/v[2])*exp((x-v[1])/v[2] - exp((x - v[1])/v[2])),col=2,add=T,xlim=range(tab$x))
+
+
+
+
+──────────────────────────────────────────────────────────────────────────
+
+─────────────
+
+File writing
+
+write(x, file = "data",
+      ncolumns = if(is.character(x)) 1 else 5,
+      append = FALSE, sep = " ")
+
+
+dev.print(pdf,'filename.pdf')
+
+
+
+
+
+──────────────────────────────────────────────────────────────────────────
+
+─────────────
+Axis Formatting
+
+# Add minor tick marks
+library(Hmisc)
+minor.tick(nx=n, ny=n, tick.ratio=n)
+
+
+
+
+
+
+──────────────────────────────────────────────────────────────────────────
+
+─────────────
+Importing CSV
+