A quick search turned up a blog post at Web Upd8 which explains why the official repositories lag behind:
Oracle JDK7 itself is not hosted in the PPA because that's not allowed by the new Java license (which is also the reason why it has been removed from the official Ubuntu repositories); the package in the PPA automatically downloads (and installs) Oracle Java JDK 7 from its official website and installs it on your computer, just like the flashplugin-installer package does.The PPA (personal package archive) repository to which they refer contains a package that automatically downloads and installs the current version of the Oracle Java 7 JDK. (Note that there is no comparable package to install just the JRE; you have to install the full JDK, which contains the JRE as a subset. That's fine with me, since I need the JDK for program development.)
The instructions are straightforward and worked fine for me. Once I had confirmed that Java 7 was installed and was the default choice, there was one more step. I use the Netbeans IDE for writing Java code. I could have installed the latest version with Java 7 bundled, but that's a hefty download, and my current version of Netbeans is recent enough. In Netbeans, I clicked Help > About and discovered that Netbeans was still launching with Java 6. The solution is to edit the configuration file <netbeans>/etc/netbeans.conf (where <netbeans> is the top directory of the Netbeans installation) and change the setting for netbeans_jdkhome to point to the Java 7 directory. When I restarted Netbeans, it launched with Java 7 and also changed the default Java platform for compiled code to Java 7.
Big thanks to the PPA maintainers for simplifying the process.