I have started studying radioactive decay.  When I studied alpha-particle emission from an unstable nucleus I wondered why should there be emission of helium nucleus only(alpha particle) and why not lithium nucleus or of any other element.  Is there any explanation as to why emission of helium nucleus is favourable and quite common?
It is said in many textbooks that alpha decay involves emitting alpha particles, which are very stable. Indeed, the binding energy () is higher than for $Z$-neighboring stable isotopes. But the binding energy is lower than, for example, ${}^9\mathrm{Be}$ (). My question is why aren't other nuclear compounds ejected from heavy nuclei, e.g. ${}^9\mathrm{Be}$?  The   $$e^{-\frac{4\pi}{\hbar}\frac{Ze^2}{4\pi\epsilon_0}\frac{1}{v_\alpha}}$$ decreases exponentially in $Z$, so it explains intuitively why lower-$Z$ particles would tunnel more often. Specifically, it would explain why we would see ${}^9\mathrm{Be}$ emission ${e^{-2}}\simeq 0.14$ times as often compared to ${}^4\mathrm{He}$ emission. Also, the particles need to form in the nucleus prior emissions; but with a similar binding energy per nucleon (~7.08 MeV for ${}^4\mathrm{He}$ vs. 6.47 MeV for ${}^9\mathrm{Be}$) and higher total binding energy for the ${}^9\mathrm{Be}$ nucleus, I would expect that its formation in the same order of prevalence as the alpha particle (according to Ohanian, between 0.1 and 1 alpha particles are in existence at any moment in time).  Can anyone explain this? A reference to an article/textbook would be preferable.  EDIT Same goes for ${}^{16}\mathrm{O}$ which is also a double magic isotope, as 'anna v' pointed out. For it, the Gamow factor is smaller by $e^{-4}\simeq 0.02$, and emission should still be viable.
Obfuscation is one way, but it can't protect from breaking the piracy protection security of the application. How do I make sure that the application is not tampered with, and how do I make sure that the registration mechanism can't be reverse engineered?  Also it is possible to convert a C# application to native code, and  is too costly.  C# provides lot of features, and is the ideal language for my code, so writing the whole codebase again in C++ is out of the question.  Secure certificates can be easily removed from the signed assemblies in .NET. Is torque as fundamental a concept as force? I used to think that torque and force were equally “fundamental”. In other words, my understanding was that we usually use Cartesian coordinates in many common problems because it is a convenient system, so as a result instantaneous forces which act in straight lines seem “easier” mathematically but torques require some extra “baggage”. This baggage includes typically teaching that torque is defined in terms of force.  But if say we happened to choose polar coordinates for the problem the situation would appear the other way around. So it would be arbitrary if we chose to define forces in terms of torques instead.  But later on I learned that angular momentum is conserved independently of regular linear momentum (IIRC). Given the definitions of force &amp; torque as derivatives of momentum, this makes it seem much less certain that one should define either torque in terms of force or vice versa — it gives the impression they are more distinct than it first seemed.  That said, as far as I know a lot of physics is about defining &amp; describing “fundamental forces” — not “fundamental torques”.   So is choosing to use either force or torque as the basis of laws &amp; problems arbitrary? Or is there an actual fundamental rationale to when one or the other should be used? java.net.SocketException: Connection reset I am getting the following error trying to read from a socket. I'm doing a readInt() on that InputStream, and I am getting this error. Perusing the documentation this suggests that the client part of the connection closed the connection. In this scenario, I am the server.  I have access to the client log files and it is not closing the connection, and in fact its log files suggest I am closing the connection. So does anybody have an idea why this is happening? What else to check for? Does this arise when there are local resources that are perhaps reaching thresholds?    I do note that I have the following line:  socket.setSoTimeout(10000);   just prior to the readInt(). There is a reason for this (long story), but just curious, are there circumstances under which this might lead to the indicated error? I have the server running in my IDE, and I happened to leave my IDE stuck on a breakpoint, and I then noticed the exact same errors begin appearing in my own logs in my IDE.  Anyway, just mentioning it, hopefully not a red herring. :-( Here's an example:  Double d = (1/3); System.out.println(d);   This returns 0, not 0.33333... as it should.  Does anyone know? Resizing videos with ffmpeg/avconv to fit into static sized player I have a html 5 video player which is 700px wide, 400px high. I'm trying to use avconv to use ffmpeg to resize (while retaining the aspect ratio) and making sure it fits into my player.  Input can be a file of any size, so I need to resize the larger ones but center the smaller ones with black bars. So far I've tried: -s and -aspect, I've seen pad being used with the -vf switch but don't understand how it works enough to get what I need.    This is a rough idea of what I need. I'm not sure if it's even possible. It's almost like CSS's max-width/max-height. I realise this may just be a jumble of words but if anyone happens to understand what I'm talking about, I'd appreciate help, Thanks.  avconv command:  avconv -y -i control.avi -vcodec libx264 -b 2000k -bufsize 20M -acodec aac -strict experimental -ar 44100 -ab 256k bigbuck_out.mp4 So I wish to create and object and set it's shading to 'smooth' using python. It seems simple enough but after trying every method I could find on the internet none of them worked for me. Here's a short example script where the object needs to have smooth shading:  import bpy from mathutils import Vector  verts = [(0,0,0),(0,5,0),(0.25,5,0),(0.25,0,0),(0,0,5),(0,5,5),(0.25,5,5),(0.25,0,5)] faces = [(0,1,2,3), (4,5,6,7), (0,4,5,1), (1,5,6,2), (2,6,7,3), (3,7,4,0)]  grat1mesh = bpy.data.meshes.new("grat1") grat1obj = bpy.data.objects.new("grat1", grat1mesh) grat1obj.location = (5, -5, 0) bpy.context.scene.objects.link(grat1obj) grat1mesh.from_pydata(verts,[],faces) grat1mesh.update(calc_edges=True)  grat2obj = grat1obj.copy() grat2obj.data = grat1mesh.copy() bpy.context.scene.objects.link(grat2obj) grat2obj.location += Vector((-0.125, 1.25, 1.25)) grat2obj.scale = (2, 0.5, 0.5)  bm = grat1obj.modifiers.new("Chop", 'BOOLEAN') bm.object = grat2obj bm.operation = 'DIFFERENCE' bpy.context.scene.objects.active = grat1obj bpy.ops.object.modifier_apply(modifier=bm.name) bpy.context.scene.objects.unlink(grat2obj)   I found this online and tried to place it at the end of the script:  smoothings = [] smoothings.append(face.use_smooth) me_ob.faces.foreach_set("use_smooth", smoothings)   However this just returned an error on the second line, perhaps as it was from an older website. Obviously using a simple bpy.ops.object.shade_smooth() didn't work and I'm kind of stumped as of what to do here! I want to construct a field with $125$ elements. My idea is to consider the polynomial ring $\Bbb F_5[x]$. It is enough to find an irreducible polynomial $f\in \Bbb F_5[x]$ of degree $3$ because then $\Bbb F_5[x]/(f)$ is a field with exactly $5^3=125$ elements.  How do I find an irreducible polynomial of degree $3$ in $\Bbb F_5[x]$? "Accountsd wants to use the 'iCloud' keychain" I, too, am suddenly getting this message.  I don't see a Keychain First Aid option in Keychain, and the two Login Keychain Settings were already unlocked.  Any other ideas for what the error message is all about, and what I should do about it? Viruses in wine? Skip certain tables with mysqldump Find the last $2$ digits of $$\large7^{7^{7^{10217}}}$$   So far I have: $17\cdot 601=10217$ and $7=7 \pmod{10}$. Any help greatly appreciated. How to create a bootable USB stick? I have accounts in Stack Overflow, Programmers, Unix &amp; Linux and Area 51. I don't want to continue my Area 51 account, so I planned to delete my Area 51 account. I have performed the following steps to delete my account, but I couldn't!  Case 1     If your account has votes or posts do the following steps:         Edit the "About Me" section of your profile to say “please delete me”.   Contact the SE support to request deletion.      I edited my "About Me" section to "please delete me". When I contacted SE Support to delete my account, I couldn't make a request. I am getting the following error:  This operation is incomplete. please do it in main site.   For deleting Area 51 account, when I do it main site, in link for deletion column I gave the Area 51 link. It says that:  it is not valid link!   Case 2     If the account has not interacted with the site yet (votes or posts), click on the delete button on your user page next to the edit link.   I am not eligible for this case!  Then how to delete my Area 51 account? Any help is appreciated! How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference Suppose Pat is male. Which one is correct?     I found out Pat is male.      I found out Pat was male.   Does the following change make any difference?     She said Pat is male.      She said Pat was male.   Suppose you created a mathematical model. When you are describing a result, which one (or neither) is correct?     The model analysis shows that the equilibrium is stable.      The model analysis showed that the equilibrium is stable. Verify that $4(29!)+5!$ is divisible by $31$. What is the difference between necessary and sufficient conditions? If $p\implies q$ ("$p$ implies $q$"), then $p$ is a sufficient condition for $q$. 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MS office restriction    This is best choice but can't protect from file uploading.   Almost I found the solution. Way is combination of MS office restriction and restrict access from browsers using firewall or antivirus. But I don't exact how to do this. What is the preferred way to remove spaces from a string in C++? I could loop through all the characters and build a new string, but is there a better way?